Method for image interpolation using asymmetric interpolation filter and apparatus therefor

ABSTRACT

A sub-pel-unit image interpolation method using a transformation-based interpolation filter includes, selecting, based on a sub-pel-unit interpolation location in a region supported by a plurality of interpolation filters for generating at least one sub-pel-unit pixel value located between integer-pel-unit pixels, one of a symmetric interpolation filter and an asymmetric interpolation filter from among the plurality of interpolation filters; and using the selected interpolation filter to generate the at least one sub-pel-unit pixel value by interpolating the integer-pel-unit pixels.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.14/130,157 filed on Jan. 14, 2014, which is a national stage entry ofInternational Application No. PCT/KR2012/005135, filed on Jun. 28, 2012,and which claims the benefit of U.S. Provisional Application No.61/502,056, filed on Jun. 28, 2011, in the U.S. Patent and TrademarkOffice the disclosures of which are incorporated herein by reference intheir entireties.

FIELD

Exemplary embodiments relate to prediction encoding using motioncompensation.

BACKGROUND ART

In typical image encoding and decoding methods, in order to encode animage, one picture is split into macro blocks. After that, predictionencoding is performed on each macro block by using inter prediction orintra prediction.

Inter prediction refers to a method of compressing an image by removingtemporal redundancy between pictures and its representative example ismotion estimation encoding. In motion estimation encoding, each block ofa current picture is predicted by using at least one reference picture.A reference block that is most similar to a current block is foundwithin a predetermined search range by using a predetermined evaluationfunction.

A current block is predicted based on a reference block, and a residualblock obtained by subtracting from the current block a prediction blockgenerated as a prediction result is encoded. In this case, in order tomore accurately perform prediction, interpolation is performed on arange of searching the reference picture, sub-pel-unit pixels smallerthan integer-pel-unit pixels are generated, and inter prediction isperformed on the generated sub-pel-unit pixels.

SUMMARY

Exemplary embodiments provide a method and apparatus for determiningfilter coefficients of a symmetric or asymmetric interpolation filter soas to generate a sub-pel-unit pixel by interpolating integer-pel-unitpixels.

According to an aspect of one or more exemplary embodiments, there isprovided an image interpolation method which is performable by using atransformation-based interpolation filter, the method includingselecting, from among a plurality of interpolation filters, and based ona sub-pel-unit interpolation location in a region which is supported bythe plurality of interpolation filters which are configured forgenerating at least one sub-pel-unit pixel value located betweeninteger-pel-unit pixels, one of a symmetric interpolation filter and anasymmetric interpolation filter; and using the selected interpolationfilter to generate the at least one sub-pel-unit pixel value byinterpolating the integer-pel-unit pixels.

In order to efficiently perform image interpolation, from among aplurality of interpolation filters which are configured for generating asub-pel-unit pixel value, an interpolation filter is variably selectedbased on a sub-pel-unit interpolation location. The interpolation filtermay be an odd- or even-number-tap interpolation filter in order toperform sub-pel-unit interpolation. The interpolation filter may beselected as a symmetric interpolation filter or as an asymmetricinterpolation filter, based on an interpolation location.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram of an image interpolation apparatus, accordingto an exemplary embodiment;

FIG. 2 is a diagram which illustrates a relationship between aninteger-pel unit and a sub-pel unit;

FIG. 3 is a diagram which illustrates adjacent integer-pel-unit pixelsto be referred to so as to determine a sub-pel-unit pixel value,according to an exemplary embodiment;

FIGS. 4A, 4B, and 4C are diagrams which illustrate examples ofinteger-pel-unit pixels to be referred to so as to determine asub-pel-unit pixel value, according to an exemplary embodiment;

FIG. 5A is a diagram which illustrates an interpolation filtering methodusing reference pixels asymmetrically located with respect to aninterpolation location in order to determine a sub-pel-unit pixel value,according to an exemplary embodiment;

FIG. 5B is a diagram which illustrates an interpolation method using aninterpolation filter including an odd number of filter coefficients inorder to determine a sub-pel-unit pixel value, according to an exemplaryembodiment;

FIG. 6 is a graph of a smoothing factor based on a smoothing parameterof a smoothed interpolation filter, according to an exemplaryembodiment;

FIG. 7 is an amplitude frequency response graph of interpolationfilters, according to an exemplary embodiment;

FIG. 8 is a flowchart which illustrates an image interpolation method,according to an exemplary embodiment;

FIGS. 9A, 9B, 9C, and 9D respectively show filter coefficients of 3-tapthrough 6-tap interpolation filters determined based on an interpolationlocation and a window filter size, according to exemplary embodiments;

FIGS. 10A, 10B, and 10C respectively show filter coefficients of 7-tapinterpolation filters determined based on an interpolation location anda window filter size, according to exemplary embodiments;

FIGS. 11A, 11B, and 11C respectively show filter coefficients of 8-tapinterpolation filters determined based on an interpolation location anda window filter size, according to exemplary embodiments;

FIGS. 12A and 12B respectively show filter coefficients of a regularizedluma interpolation filter and a regularized chroma interpolation filter,according to exemplary embodiments;

FIG. 13A is a block diagram of a video encoding apparatus using aninterpolation filter, according to an exemplary embodiment;

FIG. 13B is a block diagram of a video decoding apparatus using aninterpolation filter, according to an exemplary embodiment;

FIG. 14A is a flowchart which illustrates an image encoding method usingan interpolation filter, according to an exemplary embodiment.

FIG. 14B is a flowchart which illustrates an image decoding method usingan interpolation filter, according to an exemplary embodiment.

FIG. 15 is a diagram which illustrates a concept of coding units,according to an exemplary embodiment;

FIG. 16 is a block diagram of an image encoder based on coding units,according to an exemplary embodiment;

FIG. 17 is a block diagram of an image decoder based on coding units,according to an exemplary embodiment;

FIG. 18 is a diagram which illustrates deeper coding units according todepths and partitions, according to an exemplary embodiment;

FIG. 19 is a diagram which illustrates a relationship between a codingunit and transformation units, according to an exemplary embodiment;

FIG. 20 is a diagram which illustrates encoding information of codingunits which correspond to a coded depth, according to an exemplaryembodiment;

FIG. 21 is a diagram of deeper coding units according to depths,according to an exemplary embodiment;

FIGS. 22, 23, and 24 are diagrams which illustrate a relationshipbetween coding units, prediction units, and transformation units,according to an exemplary embodiment;

FIG. 25 is a diagram which illustrates a relationship between a codingunit, a prediction unit or a partition, and a transformation unit,according to coding mode information of Table 1;

FIG. 26 is a flowchart which illustrates a video encoding method usingan interpolation filter based on coding units having a tree structure,according to an exemplary embodiment; and

FIG. 27 is a flowchart which illustrates a video decoding method usingan interpolation filter based on coding units having a tree structure,according to an exemplary embodiment.

DETAILED DESCRIPTION

According to an aspect of one or more exemplary embodiments, there isprovided an image interpolation method which is performable by using atransformation-based interpolation filter, the method includingselecting, from among a plurality of interpolation filters, and based ona sub-pel-unit interpolation location in a region which is supported bythe plurality of interpolation filters which are configured forgenerating at least one sub-pel-unit pixel value located betweeninteger-pel-unit pixels, one of a symmetric interpolation filter and anasymmetric interpolation filter; and using the selected interpolationfilter to generate the at least one sub-pel-unit pixel value byinterpolating the integer-pel-unit pixels.

The symmetric interpolation filter may include the same number of filtercoefficients on both sides of the interpolation location in a regionwhich is supported by the symmetric interpolation filter, and theasymmetric interpolation filter may include different numbers of filtercoefficients on either side of the interpolation location in a regionwhich is supported by the asymmetric interpolation filter.

The generating of the at least one sub-pel-unit pixel value may include,if the asymmetric interpolation filter is selected, performing filteringby using filter coefficients of the asymmetric interpolation filter tosupport integer-pel-unit pixels asymmetrically located at both sides ofthe interpolation location in a region supported by the asymmetricinterpolation filter; and, if the symmetric interpolation filter isselected, performing filtering by using filter coefficients of thesymmetric interpolation filter to support integer-pel-unit pixelssymmetrically located at both sides of the interpolation location in aregion supported by the symmetric interpolation filter.

The generating of the at least one sub-pel-unit pixel value may include,if an asymmetric odd-number-tap interpolation filter which includes anodd number of filter coefficients is selected from among the pluralityof interpolation filters, performing filtering by using the odd numberof filter coefficients of the asymmetric odd-number-tap interpolationfilter to support an odd number of integer-pel-unit pixels located onboth sides of the interpolation location in a region supported by theasymmetric odd-number-tap interpolation filter; and, if a symmetriceven-number-tap interpolation filter which includes an even number offilter coefficients is selected from among the plurality ofinterpolation filters, performing filtering by using the even number offilter coefficients of the symmetric even-number-tap interpolationfilter to support an even number of integer-pel-unit pixels located onboth sides of the interpolation location in a region supported by thesymmetric even-number-tap interpolation filter.

Each of the interpolation filters may include, in order to interpolatethe integer-pel-unit pixels in a spatial domain, filter coefficientswhich are obtained by combining a filter which uses a plurality of basisfunctions for transformation and inverse transformation, and at leastone of an asymmetric window filter and a symmetric window filter.

The selecting of the interpolation filter may include selecting, fromamong the plurality of interpolation filters, an interpolation filterwhich is regularized in order to minimize a frequency response errorgenerated as an interpolation result using the selected interpolationfilter, and the regularized interpolation filter may include at leastone of i) a ¼-pel-unit interpolation filter including 7-tap filtercoefficients {−1, 4, −10, 58, 17, −5, 1} and having a window size of8.7, and ii) a ½-pel-unit interpolation filter including 8-tap filtercoefficients {−1, 4, −11, 40, 40, −11, 4, −1} and having a window sizeof 9.5.

According to another aspect of one or more exemplary embodiments, thereis provided an image interpolation apparatus which uses atransformation-based interpolation filter, the apparatus including afilter selector which is configured for selecting, from among aplurality of interpolation filters and based on a sub-pel-unitinterpolation location in a region which is supported by the pluralityof interpolation filters which are configured for generating at leastone sub-pel-unit pixel value located between integer-pel-unit pixels,one of a symmetric interpolation filter and an asymmetric interpolationfilter; and an interpolator which is configured for generating the atleast one sub-pel-unit pixel value by using the selected interpolationfilter to interpolate the integer-pel-unit pixels.

According to another aspect of one or more exemplary embodiments, thereis provided a video encoding apparatus which uses an image interpolationfilter, the apparatus including an encoder which is configured forselecting, for each block of an input picture, from among a plurality ofinterpolation filters and based on a sub-pel-unit interpolation locationin a region supported by the plurality of interpolation filters whichare configured for generating at least one sub-pel-unit pixel valuelocated between integer-pel-unit pixels, one of a symmetricinterpolation filter and an asymmetric interpolation filter, generatingthe at least one sub-pel-unit pixel value by using the selectedinterpolation filter to interpolate the integer-pel-unit pixels,performing prediction encoding, and performing transformation andquantization on a prediction result based on the prediction encoding; anoutput component which is configured for outputting a bitstreamgenerated by performing entropy encoding on quantized transformationcoefficients and encoding information; and a storage component which isconfigured for storing respective filter coefficients of the pluralityof interpolation filters.

According to another aspect of one or more exemplary embodiments, thereis provided a video decoding apparatus which uses an image interpolationfilter, the apparatus including a receiver and extractor which areconfigured for receiving an encoded bitstream of a video, performingentropy decoding and parsing, and extracting encoding information andencoded data of a picture of the video; a decoder which is configuredfor performing inverse quantization and inverse transformation onquantized transformation coefficients of the encoded data of a currentblock of the picture, selecting, from among a plurality of interpolationfilters and based on a sub-pel-unit interpolation location in a regionsupported by the plurality of interpolation filters which are configuredfor generating at least one sub-pel-unit pixel value located betweeninteger-pel-unit pixels, one of a symmetric interpolation filter and anasymmetric interpolation filter, generating the at least onesub-pel-unit pixel value by using the selected interpolation filter tointerpolate the integer-pel-unit pixels, and performing predictiondecoding in order to restore the picture; and a storage component whichis configured for storing respective filter coefficients of theplurality of interpolation filters.

According to another aspect of one or more exemplary embodiments, thereis provided a non-transitory computer readable recording medium havingrecorded thereon a program for executing the above method.

In the following description, an ‘image’ may comprehensively refer to amoving image such as a video, and/or a still image.

Interpolation using an asymmetric interpolation filter and a symmetricinterpolation filter in consideration of smoothing, according to anexemplary embodiment, is disclosed with reference to FIGS. 1 through12B. Also, video encoding and decoding using an asymmetric interpolationfilter and a symmetric interpolation filter, according to an exemplaryembodiment, are disclosed with reference to FIGS. 13A through 27. Moreparticularly, video encoding and decoding using an asymmetricinterpolation filter and a symmetric interpolation filter based oncoding units having a tree structure, according to an exemplaryembodiment, are disclosed with reference to FIGS. 15 through 25.

Interpolation using an asymmetric interpolation filter and a symmetricinterpolation filter in consideration of smoothing, according to anexemplary embodiment, will now be described in detail with reference toFIGS. 1 through 12B.

FIG. 1 is a block diagram of an image interpolation apparatus 10,according to an exemplary embodiment.

The image interpolation apparatus 10 using symmetric and asymmetricinterpolation filters includes a filter selector 12 and an interpolator14. Operations of the filter selector 12 and the interpolator 14 of theimage interpolation apparatus 10 may be cooperatively controlled by avideo encoding processor, a central processing unit (CPU), and a graphicprocessor.

The image interpolation apparatus 10 may receive an input image and maygenerate sub-pel-unit pixel values by interpolating integer-pel-unitpixels. The input image may include any one or more of a picturesequence, a picture, a frame, and/or blocks of a video.

The filter selector 12 may variably select an interpolation filter forgenerating at least one sub-pel-unit pixel value located betweeninteger-pel units, based on a sub-pel-unit interpolation location.

The interpolator 14 may interpolate integer-pel-unit pixels adjacent tothe sub-pel-unit interpolation location by using the interpolationfilter selected by the filter selector 12, thereby generatingsub-pel-unit pixel values. Interpolation filtering of integer-pel-unitpixels to generate sub-pel-unit pixel values may include interpolationfiltering of integer-pel-unit reference pixel values includinginteger-pel-unit pixels adjacent to the sub-pel-unit interpolationlocation in a region supported by the interpolation filter.

The interpolation filter may include filter coefficients fortransforming integer-pel-unit reference pixels based on a plurality ofbasis functions, and for inversely transforming a plurality ofcoefficients generated as a transformation result.

The interpolation filter may be a one-dimensional filter or atwo-dimensional filter. If the selected interpolation filter is aone-dimensional filter, the interpolator 14 may continuously performfiltering by using one-dimensional interpolation filters in two or moredirections, thereby generating a current sub-pel-unit pixel value.

The filter selector 12 may individually select an interpolation filterbased on the sub-pel-unit interpolation location. The interpolationfilter may include a symmetric interpolation filter which includes thesame numbers of filter coefficients on both sides of an interpolationlocation in a region supported by the symmetric interpolation filter,and an asymmetric interpolation filter which includes different numbersof filter coefficients on either side of an interpolation location in aregion supported by the asymmetric interpolation filter. The filterselector 12 may individually select a symmetric interpolation filter andan asymmetric interpolation filter based on the sub-pel-unitinterpolation location.

For example, a 7-tap interpolation filter may include three filtercoefficients and four filter coefficients on either side of aninterpolation location in a region supported by the 7-tap interpolationfilter. In this case, the 7-tap interpolation filter may be regarded asan asymmetric interpolation filter.

For example, an 8-tap interpolation filter may include four filtercoefficients on each side of an interpolation location in a regionsupported by the 8-tap interpolation filter. In this case, the 8-tapinterpolation filter may be regarded as a symmetric interpolationfilter.

If the filter selector 12 selects an asymmetric interpolation filter,the interpolator 14 may perform filtering on integer-pel-unit pixelswhich are asymmetrically located with respect to an interpolationlocation. Conversely, if a symmetric interpolation filter is selected,the interpolator 14 may perform filtering on integer-pel-unit pixelswhich are symmetrically located with respect to an interpolationlocation.

The interpolation filter may include an asymmetric odd-number-tapinterpolation filter which includes an odd number of filtercoefficients, and a symmetric even-number-tap interpolation filter whichincludes an even number of filter coefficients. The filter selector 12may individually select an asymmetric odd-number-tap interpolationfilter and a symmetric even-number-tap interpolation filter based on thesub-pel-unit interpolation location. For example, a ½-pel-unitinterpolation filter and a ¼-pel-unit interpolation filter may beindividually and variably selected. Thus, an 8-tap interpolation filter,i.e., a symmetric even-number-tap interpolation filter, may be selectedas the ½-pel-unit interpolation filter, and a 7-tap interpolationfilter, i.e., an asymmetric odd-number-tap interpolation filter, may beselected as the ¼-pel-unit interpolation filter.

In order to interpolate integer-pel-unit pixels in a spatial domain,each interpolation filter may be obtained by combining filtercoefficients for performing transformation and inverse transformation byusing a plurality of basis functions, and window filter coefficients forperforming low pass filtering.

The interpolation filter may be generated based on a window filter thatis asymmetric with respect to an interpolation location or a windowfilter that is symmetric with respect to an interpolation location.

The asymmetric interpolation filter may also be generated by combining afilter for performing transformation and inverse transformation based ona plurality of basis functions with an asymmetric window filter.

If an odd-number-tap interpolation filter is selected, the interpolator14 may perform filtering on an odd number of integer-pel-unit pixelslocated with respect to an interpolation location, by using an oddnumber of filter coefficients of the odd-number-tap interpolationfilter.

If an even-number-tap interpolation filter is selected, the interpolator14 may perform filtering on an even number of integer-pel-unit pixelslocated with respect to an interpolation location, by using an evennumber of filter coefficients of the even-number-tap interpolationfilter.

The odd-number-tap interpolation filter may include different numbers offilter coefficients on either side of an interpolation location in acorresponding supporting region and thus may be an asymmetricinterpolation filter. The even-number-tap interpolation filter may be asymmetric interpolation filter which includes the same number of filtercoefficients on both sides of an interpolation location in acorresponding supporting region.

The filter selector 12 may select an interpolation filter which isregularized in order to minimize a frequency response error generated asan interpolation result when using the interpolation filter. Forexample, the regularized interpolation filter may include at least oneof i) a ¼-pel-unit interpolation filter including 7-tap filtercoefficients {−1, 4, −10, 58, 17, −5, 1} and having a window size of8.7, and ii) a ½-pel-unit interpolation filter including 8-tap filtercoefficients {−1, 4, −11, 40, 40, −11, 4, −1} and having a window sizeof 9.5.

Further, the filter selector 12 may individually and variably select aninterpolation filter based on color components. For example, theregularized interpolation filter for luma pixels may be determined as a¼-pel-unit 7-tap interpolation filter and a ½-pel-unit 8-tapinterpolation filter. The regularized interpolation filter for chromapixels may be determined as ⅛-pel-unit, ¼-pel-unit, and ½-pel-unit 4-tapinterpolation filters.

The determined regularized interpolation filter for chroma pixels mayinclude i) a ⅛-pel-unit interpolation filter including 4-tap filtercoefficients {−2, 58, 10, −2} for a ⅛ interpolation location and havinga smoothness of 0.012, ii) a ¼-pel-unit interpolation filter including4-tap filter coefficients {−4, 54, 16, −2} for a ¼ interpolationlocation and having a smoothness of 0.016, iii) a ⅛-pel-unitinterpolation filter including 4-tap filter coefficients {−6, 46, 28,−4} for a ⅜ interpolation location and having a smoothness of 0.018, andiv) a ½-pel-unit interpolation filter including 4-tap filtercoefficients {−4, 36, 36, −4} for a ½ interpolation location and havinga smoothness of 0.020.

The interpolation filter may be a mirror-reflective symmetric filter inwhich a filter coefficient f(α) of an the interpolation location α and afilter coefficient f_(l)(1−α) of an interpolation location (1−α) may bethe same.

The ¼-pel-unit interpolation filter for luma pixels may be amirror-reflective symmetric filter. Accordingly, an interpolation filterfor a ¼ interpolation location and an interpolation filter for a ¾interpolation location may include symmetrically the same coefficients.If a ¼-pel-unit 7-tap luma interpolation filter includes filtercoefficients {−1, 4, −10, 58, 17, −5, 1} of a ¼ interpolation location,it may include filter coefficients {1, −5, 17, 58, −10, 4, −1} of a ¾interpolation location.

The ⅛-pel-unit interpolation filter for chroma pixels may be amirror-reflective symmetric filter. Accordingly, an interpolation filterfor a ⅛ interpolation location and an interpolation filter for a ⅞interpolation location may include symmetrically the same coefficients.Similarly, an interpolation filter for a ⅜ interpolation location and aninterpolation filter for a ⅝ interpolation location may includesymmetrically the same coefficients. The interpolation filter may bedetermined based on a transformation-based interpolation filter whichincludes filter coefficients determined by using a plurality of basisfunctions. Further, a smoothed interpolation filter modified from thetransformation-based interpolation filter may be used to performfiltering by varying its smoothness based on the distance between aninterpolation location and integer-pel-unit pixels.

The smoothness of the smoothed interpolation filter may be determinedbased on the distance between an interpolation location andinteger-pel-unit pixels. The interpolation filter may include differentfilter coefficients which are based on the sub-pel-unit interpolationlocation and its smoothness.

The smoothness of the smoothed interpolation filter may also bedetermined based on the distance between an interpolation location andinteger-pel-unit pixels adjacent to the interpolation location.

Further, the interpolation filter may include filter coefficients forallowing integer-pel-unit reference pixels, which are away from theinterpolation location, to be smoothed.

The smoothed interpolation filter obtained by combining filtercoefficients for performing transformation and inverse transformationand window filter coefficients for performing low pass filtering mayinclude filter coefficients for giving a large weight to ainteger-pel-unit reference pixel close to the interpolation location andgiving a small weight to a integer-pel-unit reference pixel away fromthe interpolation location.

The smoothed interpolation filter may include filter coefficients forsmoothing integer-pel-unit reference pixels, transforming the smoothedinteger-pel-unit reference pixels by using a plurality of basisfunctions, and inversely transforming a plurality of coefficientsgenerated as a transformation result.

The smoothed interpolation filter may include different filtercoefficients which are determined based on its length and based on thesub-pel-unit interpolation location and its smoothness.

Further, the smoothed interpolation filter may include different filtercoefficients which are determined based on a scaling ratio as aninterpolation result, and based on the sub-pel-unit interpolationlocation, its smoothness, and its length. The filter selector 12 mayselect a smoothed interpolation filter of which filter coefficients areincreased to integers. The interpolator 14 regularizes pixel valuesgenerated by using the smoothed interpolation filter selected by thefilter selector 12.

Also, the filter selector 12 may variably select an interpolation filterbased on pixel characteristics. The interpolator 14 may generatesub-pel-unit pixel values by using the interpolation filter which isselected based on pixel characteristics.

The interpolation filter which is selectable by the filter selector 12may include a smoothed interpolation filter and a general interpolationfilter that does not consider smoothing. Thus, based on respective imagecharacteristics, the filter selector 12 may select a generalinterpolation filter that does not consider smoothing at all.

For example, according to another exemplary embodiment, the imageinterpolation apparatus 10 may perform image interpolation by usingdifferent interpolation filters based on color components.

According to another exemplary embodiment, the filter selector 12 mayvariably select an interpolation filter based on the sub-pel-unitinterpolation location and a color component of a current pixel.According to another exemplary embodiment, the interpolator 14 mayinterpolate integer-pel-unit pixels by using the selected interpolationfilter, thereby generating at least one sub-pel-unit pixel value.

For example, the filter selector 12 may variably determine aninterpolation filter for a luma component and an interpolation filterfor a chroma component.

In order to interpolate a chroma pixel, the filter selector 12 mayselect a smoothed interpolation filter having a greater smoothness thanthat of an interpolation filter for a luma pixel.

Further, in order to interpolate a chroma pixel, an interpolation filterincluding filter coefficients determined based on a smoothing parameterhaving a greater smoothness than that of an interpolation filter for aluma pixel, or an interpolation filter including filter coefficientscombined with a window filter for removing more high-frequencycomponents than an interpolation filter for a luma pixel may beselected.

In order to obtain a smooth interpolation result of a chroma component,a smoothed interpolation filter obtained by combining filtercoefficients for performing transformation and inverse transformationbased on a plurality of basis functions, and window filter coefficientsfor performing low pass filtering, may be selected.

The image interpolation apparatus 10 may include a CPU (not shown) forcomprehensively controlling the filter selector 12 and the interpolator14. Alternatively, the filter selector 12 and the interpolator 14 may bedriven by individual processors (not shown) and the processors mayoperate cooperatively with each other, thereby operating the whole imageinterpolation apparatus 10. Alternatively, a processor (not shown)outside the image interpolation apparatus 10 may control the filterselector 12 and the interpolator 14.

The image interpolation apparatus 10 may include one or more datastorage units (not shown) for storing input/output (I/O) data of thefilter selector 12 and the interpolator 14. The image interpolationapparatus 10 may also include a memory controller (not shown) forcontrolling data I/O of the data storage units (not shown).

The image interpolation apparatus 10 may include an additional processorwhich includes a circuit for performing image interpolation.Alternatively, the image interpolation apparatus 10 may include astorage medium on which an image interpolation module is recorded, andthe CPU may call and drive the image interpolation module so as toperform image interpolation.

Image interpolation is used to transform a low-quality image into ahigh-quality image, to transform an interlaced image into a progressiveimage, and/or to up-sample a low-quality image into a high-qualityimage. Further, when a video encoding apparatus encodes an image, amotion estimator and compensator may perform inter prediction by usingan interpolated reference frame. The accuracy of inter prediction may beincreased by interpolating a reference frame to generate a high-qualityimage, and performing motion estimation and compensation based on thehigh-quality image. Similarly, when an image decoding apparatus decodesan image, a motion compensator may perform motion compensation by usingan interpolated reference frame, thereby increasing the accuracy ofinter prediction.

In addition, the smoothed interpolation filter used by the imageinterpolation apparatus 10 may obtain a smooth interpolation result byreducing high-frequency components in an interpolation result using aninterpolation filter. Because the high-frequency components reduce theefficiency of image compression, the efficiency of image encoding anddecoding may also be improved by performing smoothness-adjustable imageinterpolation.

Further, a symmetric interpolation filter in which filter coefficientsare symmetrically located with respect to an interpolation location oran asymmetric interpolation filter in which filter coefficients areasymmetrically located with respect to an interpolation location may beselectively used. Also, as an interpolation filter, an odd-number-tapinterpolation filter or an even-number-tap interpolation filter may beselectively used based on an interpolation location. Accordingly, theimage interpolation apparatus 10 may perform image interpolationfiltering on integer-pel-unit pixels asymmetrically located with respectto an interpolation location as well as integer-pel-unit pixelssymmetrically located with respect to an interpolation location.

Interpolation using an interpolation filter obtained by combining filtercoefficients for performing transformation and inverse transformationbased on a plurality of basis functions with window filter coefficients,according to exemplary embodiments, will now be described in detail withreference to FIGS. 2 through 7B.

FIG. 2 is a diagram which illustrates a relationship between aninteger-pel unit and a sub-pel unit.

Referring to FIG. 2, the image interpolation apparatus 10 generatespixel values of locations ‘X’ by interpolating integer-pel-unit pixelvalues of locations ‘◯’ of a predetermined block 20 in a spatial domain.The pixel values of the locations ‘X’ are sub-pel-unit pixel values ofinterpolation locations determined by αx and αy. Although FIG. 2illustrates that the predetermined block 20 is a 4×4 block, it will beunderstood by one of ordinary skill in the art that the block size isnot limited to 4×4 and may be greater or smaller than 4×4.

In video processing, a motion vector is used to perform motioncompensation and prediction on a current image. According to predictionencoding, a previously decoded image is referred to so as to predict acurrent image, and a motion vector indicates a predetermined point of areference image. Therefore, a motion vector indicates aninteger-pel-unit pixel of a reference image.

However, a pixel to be referred to by a current image may be locatedbetween integer-pel-unit pixels of a reference image. Such a location isreferred to as a sub-pel-unit location. Because a pixel does not existat a sub-pel-unit location, a sub-pel-unit pixel value is merelypredicted by using integer-pel-unit pixel values. In other words, asub-pel-unit pixel value is estimated by interpolating integer-pel-unitpixels.

A method for interpolating integer-pel-unit pixels will now be describedin detail with reference to FIGS. 3, 4A, 4B, and 4C.

FIG. 3 is a diagram which illustrates adjacent integer-pel-unit pixelsto be referred to so as to determine a sub-pel-unit pixel value,according to an exemplary embodiment.

Referring to FIG. 3, the image interpolation apparatus 10 generates asub-pel-unit pixel value 35 of an interpolation location byinterpolating integer-pel-unit pixel values 31 and 33 in a spatialdomain. The interpolation location is determined by a.

FIGS. 4A, 4B, and 4C are diagrams which illustrate examples ofinteger-pel-unit pixels to be referred to so as to determine asub-pel-unit pixel value, according to an exemplary embodiment.

Referring to FIG. 4A, in order to generate the sub-pel-unit pixel value35 by interpolating the two integer-pel-unit pixel values 31 and 33, aplurality of adjacent integer-pel-unit pixels values 37 and 39,including the integer-pel-unit pixel values 31 and 33, are used. Inother words, zero-th and first pixels may be interpolated by performingone-dimensional interpolation filtering on 2M pixel values from an−(M−1)th pixel value to an Mth pixel value.

Also, although FIG. 4A illustrates that pixel values in a horizontaldirection are interpolated, one-dimensional interpolation filtering mayalternatively be performed by using pixel values in a vertical ordiagonal direction.

Referring to FIG. 4B, a pixel value P(α) of an interpolation location αmay be generated by interpolating pixels P₀ 41 and P₁ 43 that areadjacent to each other in a vertical direction. When FIGS. 4A and 4B arecompared, their interpolation filtering methods are similar, and theonly difference therebetween is that pixel values 47 and 49 aligned in avertical direction are interpolated in FIG. 4B while the pixel values 37and 39 aligned in a horizontal direction are interpolated in FIG. 4A.

Referring to FIG. 4C, similarly, a pixel value 44 of the interpolationlocation α is generated by interpolating two adjacent pixel values 40and 42. The only difference from FIG. 4A is that pixel values 46 and 48aligned in a diagonal direction are used instead of the pixel values 37and 39 aligned in a horizontal direction.

In addition to the directions shown in FIGS. 4A, 4B, and 4C,one-dimensional interpolation filtering may be performed in variousdirections.

Interpolation filtering may be performed to interpolate integer-pel-unitpixels for generating a sub-pel-unit pixel value. The interpolationfiltering may be represented by the following equation.

p(α)=f(α)×p=Σ _(−M+1) ^(M) f _(m) ·p _(m)

A pixel value p(x) is generated by performing interpolation according toa dot product of a vector p of 2M integer-pel-unit reference pixels{p_(m)}={p_(−M+1), p_(−M+2), . . . , p₀, p₁, . . . , p_(M)} and a vectorf(x) of filter coefficients {f_(m)}={f_(−M+1), f_(−M+2), . . . , f₀, f₁,. . . , f_(M)}. Because a filter coefficient f(α) varies according tothe interpolation location α and a pixel value p(α) obtained byperforming interpolation is determined based on the filter coefficientf(α), a selected interpolation filter, i.e., the determined filtercoefficient f(x), greatly influences the performance of interpolationfiltering.

Image interpolation using transformation and inverse transformationbased on basis functions, and a method for determining an interpolationfilter, will now be described in detail.

An interpolation filter using transformation and inverse transformationinitially transforms pixel values by using a plurality of basisfunctions having different frequency components. Transformation mayinclude all types of transformation from pixel values in a spatialdomain into coefficients in a transformation domain, and may includediscrete cosine transformation (DCT). Integer-pel-unit pixel values aretransformed by using a plurality of basis functions. A pixel value mayinclude either or both of a luma pixel value and a chroma pixel value.Basis functions are not limited to particular basis functions, and mayinclude all basis functions for transforming pixel values in a spatialdomain into pixel values in a transformation domain. For example, abasis function may include a cosine or sine function for performing DCTand inverse DCT (IDCT). Alternatively, various basis functions, such asa spline function and a polynomial basis function, may be used. Also,DCT may include modified DCT (MDCT) and/or MDCT with windowing.

The interpolation filter using transformation and inverse transformationshifts phases of the basis functions used to perform transformation andinversely transforms values of a plurality of coefficients generated byusing the phase-shifted basis functions, i.e., values in atransformation domain. As an inverse transformation result, pixel valuesin a spatial domain are output, and the output values may include pixelvalues of an interpolation location.

Filter Coefficients Using Orthogonal Transformation and InverseTransformation Based on Orthogonal Basis Functions

A case when the interpolator 14 performs interpolation filtering usingtransformation and inverse transformation based on orthogonal basisfunctions will now be described in detail. In particular, DCT isdescribed as an example of the transformation.

For example, referring to FIG. 4A, in order to generate the sub-pel-unitpixel value 35 by interpolating the two integer-pel-unit pixel values 31and 33, by using a plurality of adjacent integer-pel-unit pixels values37 and 39 including the integer-pel-unit pixel values 31 and 33, zero-thand first pixels may be interpolated by performing one-dimensional DCTon 2M pixel values from an −(M−1)th pixel value to an Mth pixel value,and performing one-dimensional IDCT based on phase-shifted basisfunctions.

The interpolator 14 initially performs one-dimensional DCT oninteger-pel-unit pixel values. One-dimensional DCT may be performed asrepresented in Equation 38.

$\begin{matrix}{C_{k} = {{\frac{1}{M}{\sum\limits_{l = {M + 1}}^{M}\; {{p(l)}{{\cos \left( \frac{\left( {{2\; l} - 1 + {2\; M}} \right)k\; \pi}{4\; M} \right)}.0}}}} \leq k \leq {{2\; M} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 38} \right\rbrack\end{matrix}$

p(l) represents the pixel values 37 and 39 from an −(M−1)th pixel valueto an Mth pixel value, and C_(k) represents a plurality of coefficientsin a frequency domain, which are generated by performing one-dimensionalDCT on the pixel values 37 and 39. In this case, k is a positive integerthat satisfies the above condition of Equation 38.

After one-dimensional DCT is performed on the pixel values 37 and 39 byusing Equation 38, the interpolator 14 performs inverse transformationon the coefficients as represented in Equation 39.

$\begin{matrix}{{P(\alpha)} = {\frac{C_{0}}{2} + {\sum\limits_{k = 1}^{{2\; M} - 1}\; {C_{k}{\cos \left( \frac{\left( {{2\; \alpha} - 1 + {2\; M}} \right)k\; \pi}{4\; M} \right)}}}}} & \left\lbrack {{Equation}\mspace{14mu} 39} \right\rbrack\end{matrix}$

α represents an interpolation location between two pixel values asillustrated in FIG. 13, and may have any of various fractional values,such as, for example, ½, ¼, ¾, ⅛, ⅜, ⅝, ⅞, 1/16, etc. The fractionalvalue is not limited to a particular value, and a may be a real valueinstead of a fractional value. P(α) represents the sub-pel-unit pixelvalue 35 of the interpolation location α, which is generated as aone-dimensional IDCT result.

When Equation 39 is compared to Equation 38, the phase of a cosinefunction that is a basis function used to perform IDCT is determinedbased on a fractional number a instead of an integer l, and thus isdifferent from the phase of a basis function used to performone-dimensional DCT. In particular, the phase of each basis functionused to perform inverse transformation, i.e., a cosine function, isshifted according to 2 a. If the interpolator 14 performs IDCT based onthe phase-shifted cosine functions according to Equation 39, thesub-pel-unit pixel value 35 of the interpolation location α, i.e., P(α),is generated.

DCT according to Equation 38 is expressed by a determinant representedin Equation 40.

C=D×REF  [Equation 40]

Here, C is a 2M×1 matrix of the 2M coefficients described above inrelation to Equation 38, and REF is a 2M×1 matrix of theinteger-pel-unit pixel values, i.e., P_(−(M−1)), . . . P_(M) pixelvalues, as described above in relation to Equation 38. The number ofinteger-pel-unit pixel values used to perform interpolation, i.e., 2M,refers to the number of taps of a one-dimensional interpolation filter.D is a square matrix for performing one-dimensional DCT and may bedefined as represented in Equation 4.

$\begin{matrix}{{D_{kl} = {\frac{1}{M}{\cos \left( \frac{\left( {{2\; l} + 1 + {2\; M}} \right)k\; \pi}{4\; M} \right)}}}{0 \leq k \leq {{2\; M} - 1 - \left( {M - 1} \right)} \leq l \leq M}} & \left\lbrack {{Equation}\mspace{14mu} 4} \right\rbrack\end{matrix}$

k and l are integers that satisfy the above conditions, and D_(kl)refers to a row k and a column l of the square matrix D for performingDCT in Equation 40. M is the same as that of Equation 40.

IDCT which is performed by using a plurality of phase-shifted basisfunctions according to Equation 39 is expressed by a determinantrepresented in Equation 5.

P(α)=W(α)×C  [Equation 5]

Here, P(α) is the same as that of Equation 39, and W(α) is a 1×2M matrixfor performing one-dimensional IDCT by using a plurality ofphase-shifted basis functions and may be defined as represented inEquation 6.

$\begin{matrix}{{{W_{0}(\alpha)} = \frac{1}{2}}{{{W_{k}(\alpha)} = {\cos \left( \frac{\left( {{2\; \alpha} - 1 + {2\; M}} \right)k\; \pi}{4\; M} \right)}},{1 \leq k \leq {{2\; M} - 1}}}} & \left\lbrack {{Equation}\mspace{14mu} 6} \right\rbrack\end{matrix}$

k is an integer that satisfies the above condition, and W_(k)(α) refersto a column k of the matrix W(α) as described above in relation toEquation 5. A filter F(α) for performing one-dimensional DCT andone-dimensional IDCT using a plurality of phase-shifted basis functionsbased on Equations 3 and 5 may be defined as represented in Equation 7.

$\begin{matrix}{{{P(\alpha)} = {{F(\alpha)} \times {REF}}}{{F_{l}(\alpha)} = {\sum\limits_{k = 0}^{{2\; M} - 1}\; {{W_{k}(\alpha)}D_{kl}}}}{0 \leq k \leq {{2\; M} - 1 - \left( {M - 1} \right)} \leq l \leq M}} & \left\lbrack {{Equation}\mspace{14mu} 7} \right\rbrack\end{matrix}$

k and l are integers that satisfy the above conditions, F_(l)(α) refersto a column l of F(α), and W(α) and D are the same as those of Equation40.

Interpolation Filter Coefficients for Scaled Interpolation

Various interpolation filter generation methods according to anexemplary embodiment are based on an arithmetic expression forgenerating a floating point number instead of an integer, and absolutevalues of filter coefficients are usually not greater than 1. Inparticular, a calculation result of a real number instead of an integermay be generated by a sub-pel-unit interpolation location α.

The efficiency of integer-based calculation is greater than that offloating-point-based calculation. As such, the image interpolationapparatus 10 may improve the calculation efficiency of interpolationfiltering by scaling filter coefficients into integers by using ascaling ratio. In addition, because a bit depth of pixel values isincreased, the accuracy of interpolation filtering may also be improved.

The image interpolation apparatus 10 may multiply filter coefficientsf_(m)(α) by a predetermined value, and may perform image interpolationby using large filter coefficients F_(m)(α). For example, the filtercoefficients F_(m)(α) may be scaled from the filter coefficientsf_(m)(α) as represented in Equation 8.

F _(m)(α)=int(f _(m)(α)·2^(n))  [Equation 8]

For efficiency of calculation, the scaling ratio may be in the form of2^(n). n may be equal to zero or a positive integer. An interpolationfiltering result using filter coefficients scaled by 2^(n) may have abit depth scaled by n bits in comparison to a result obtained by usingoriginal filter coefficients.

Integer calculation interpolation filtering using the scaled filtercoefficients F_(m)(α) may satisfy Equation 9. In particular, afterinterpolation filtering is performed by using the scaled filtercoefficients F_(m)(α), the scaled bit depth must be restored to anoriginal bit depth.

p(α)= (Σ_(−M+1) ^(M) F _(m)(α)·p _(m)+offset )>>n  [Equation 9]

In this case, an offset may be equal to 2^(n-1).

In particular, because an scaled filtering result using an scaledinterpolation filter must be reduced by a scaling ratio, i.e., 2^(n), soas to be restored to original bits, a bit depth of the scaled filteringresult may be reduced by n bits.

If two-step interpolation filtering is performed by performingone-dimensional interpolation filtering in a horizontal direction andperforming one-dimensional interpolation filtering in a verticaldirection, a reduction may be made by a total of 2n bits. Accordingly,if a first one-dimensional interpolation filter is scaled by n1 bits anda second one-dimensional interpolation filter is scaled by n2 bits,after two-step interpolation filtering is performed by using the firstand second one-dimensional interpolation filters, a reduction may bemade by a sum of n1 and n2, i.e., 2n bits. The first one-dimensionalinterpolation filter may be an interpolation filter that is not scaled.

Because a sum of the filter coefficients f_(m)(α) is equal to 1, asexpressed in Equation 10 below:

Σ_(−M+1) ^(M) f _(m)(α)= 1[Equation 10]

a condition for regularizing the filter coefficients F_(m)(α) of thescaled interpolation filter must satisfy Equation 11.

Σ_(−M+1) ^(M) F _(m)(α)=2^(n)  [Equation 11]

However, the regularization condition according to Equation 11 may causea rounding error. The image interpolation apparatus 10 may round off thescaled filter coefficients F_(m)(α) based on the regularizationcondition according to Equation 11. For regularization, some of thescaled filter coefficients F_(m)(α) may be adjusted within apredetermined range of original values. For example, some of the scaledfilter coefficients F_(m)(α) may be adjusted within a range of ±1 inorder to correct a rounding error.

For an interpolation filter having an odd number of reference pixels oran asymmetric interpolation filter with respect to an interpolationlocation, the interpolator 14 may change an interpolation filter usingtransformation and inverse transformation based on a plurality of basisfunctions.

Image interpolation which is performed by using an odd-number-tapinterpolation filter which includes an odd number of filter coefficientsas an interpolation filter using transformation and inversetransformation based on a plurality of basis functions will be describedbelow.

Asymmetric Interpolation Filter

FIG. 5A is a diagram which illustrates an interpolation filtering methodusing reference pixels asymmetrically located with respect to aninterpolation location in order to determine a sub-pel-unit pixel value,according to an exemplary embodiment.

It is assumed that, in order to calculate a pixel p(α) 50 of asub-pel-unit interpolation location α, left reference pixels 52 andright reference pixels 54 with respect to the interpolation location αare used to perform interpolation filtering. The number of the leftreference pixels 52 is three and the number of the right referencepixels 54 is five. Because an odd number of pixels are supported by theinterpolation filtering, the left and right reference pixels 52 and 54are asymmetrically located with respect to the interpolation location α.

As described above in relation to Equations 38 through 40 and 4 through7, interpolation filtering is performed by using 2M integer-pel-unitreference pixels p_(−M+1), p_(−M+2), . . . , p₀, p₁, . . . , p_(M) whichare symmetrically distributed with respect to the interpolation locationα. That is, if reference pixels are represented as p_(l), the range ofan integer l is represented as −M+1≦l≦M.

If the interpolation location α of Equations 38 through 40 and 4 through7 is moved in parallel translation to α−h, filter coefficients of aninterpolation filter using reference pixels asymmetrically located withrespect to the interpolation location α as illustrated in FIG. 5A may begenerated by using Equations 38 through 40 and 4 through 7.

In particular, if the asymmetric left and right reference pixels 52 and54 are represented as p_(l), the range of an integer l is −M+1+h≦l≦M+h.In this case, M is 4 and h is 1. The number of the left reference pixels52 is one less than that in a case when 2M reference pixels aresymmetrically distributed with respect to the interpolation location α.

The interpolation filter according to Equations 38 through 40 and 4through 7 is a one-dimensional filter. In order to performtwo-dimensional filtering by using the one-dimensional filter,interpolation filtering is performed in a vertical direction and in ahorizontal direction. In other words, one-dimensional interpolationfiltering is performed twice. From among the performing of theone-dimensional interpolation filtering two times, for performing motioncompensation, the second one-dimensional interpolation filtering uses afilter of which the number of filter taps is increased by a half and thefirst one-dimensional interpolation filtering is performed on anexpanded block.

When interpolation filtering is performed on a left boundary of a block,the block must be expanded leftward from the left boundary. If asymmetric interpolation filter using 2M reference pixels which aresymmetrically located with respect to the interpolation location α isused, in order to perform interpolation filtering, the block must beexpanded leftward by M pixels.

However, if an asymmetric interpolation filter using reference pixelswhich are asymmetrically located with respect to the interpolationlocation α is used, in order to perform interpolation filtering, afiltering region must be expanded leftward of the block by M−h pixels.Similarly, if h is a negative direction, when interpolation filtering isperformed on a right boundary of a block, a filtering region must beexpanded rightward of the block by M+h pixels. In other words, ifinterpolation filtering is performed on a boundary of a block, incomparison to a case when a symmetric interpolation filter is used, whenan asymmetric interpolation filter is used, a region of the block to beexpanded may be reduced. As such, a storage space for storing pixelvalues of the expanded region may be reduced, and the amount ofcalculation for expanding the block may also be reduced.

Odd-Number-Tap Interpolation Filter

FIG. 5B is a diagram which illustrates an interpolation method using aninterpolation filter including an odd number of filter coefficients inorder to determine a sub-pel-unit pixel value, according to an exemplaryembodiment.

It is assumed that, in order to calculate a pixel p(α) 55 of asub-pel-unit interpolation location α, an interpolation filter usesreference pixels {p⁻², p⁻¹, p₀, p₁, p₂}. The number of reference pixelsis five, i.e., an odd number, and three left reference pixels 51 and tworight reference pixels 53 with respect to the interpolation location αmay be referred to so as to perform interpolation filtering.

Because the left and right reference pixels 51 and 53 are asymmetricallylocated with respect to the interpolation location α and the number ofthe right reference pixels 53 is less than that of the left referencepixels 51, the interpolation filter illustrated in FIG. 5B may beeffective to perform interpolation filtering on a right boundary of ablock.

Initially, according to Equations 12 through 15 below, filtercoefficients {p(α)} of an interpolation filter using reference pixels{p_(l)} in which the range of an integer l is −M+1≦l≦M−1, and having afilter size Size (i.e., the number of filter taps) of 2M−1 aredetermined.

$\begin{matrix}{{{D_{lk} = {{{\frac{2}{size}{\cos \left( \frac{\pi \; {k\left( {l + {{Size}/2}} \right)}}{Size} \right)}} - M + 1} \leq l \leq {M - 1}}};}{0 \leq k \leq {{Size} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 12} \right\rbrack \\{{{W_{k} = {\cos \left( \frac{\pi \; {k\left( {\propto {{+ {Size}}/2}} \right)}}{Size} \right)}};}{0 \leq k \leq {{Size} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 13} \right\rbrack \\{{{Filter}_{l}( \propto )} = {\sum\limits_{k = 0}^{{Size} - 1}\; {W_{k}D_{lk}}}} & \left\lbrack {{Equation}\mspace{14mu} 14} \right\rbrack \\{{p(\alpha)} = {\sum\limits_{l = {{- M} + 1}}^{M - 1}\; {{{Filter}(\alpha)}_{l}p_{l}}}} & \left\lbrack {{Equation}\mspace{14mu} 15} \right\rbrack\end{matrix}$

If M is equal to 3, interpolation filter coefficients of FIG. 5B may bedetermined according to Equation 15.

Alternatively, according to Equations 16 through 19 below, filtercoefficients {p(α)} of an interpolation filter using reference pixels{p_(l)} in which the range of an integer l is −M+2≦l≦M, and having afilter size Size (i.e., the number of filter taps) of 2M−1 may bedetermined.

$\begin{matrix}{{{D_{lk} = {{{\frac{2}{Size}{\cos \left( \frac{\pi \; {k\left( {l + {{Size}/2}} \right)}}{Size} \right)}} - M + 2} \leq l \leq M}};}{0 \leq k \leq {{Size} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 16} \right\rbrack \\{W_{k} = {\cos \left( \frac{\pi \; {k\left( {\propto {{+ {Size}}/2}} \right)}}{Size} \right)}} & \left\lbrack {{Equation}\mspace{14mu} 17} \right\rbrack \\{{{Filter}_{l}( \propto )} = {\sum\limits_{k = 0}^{{Size} - 1}\; {W_{k}D_{lk}}}} & \left\lbrack {{Equation}\mspace{14mu} 18} \right\rbrack \\{{p(\alpha)} = {\sum\limits_{l = {{- M} + 2}}^{M}\; {{{Filter}(\alpha)}_{l}p_{l}}}} & \left\lbrack {{Equation}\mspace{14mu} 19} \right\rbrack\end{matrix}$

Interpolation filtering using the filter coefficients determinedaccording to Equation 19 may be performed on pixels moved in paralleltranslation by one to the right from the reference pixels of FIG. 5B.

In Equations 12 through 19, α is not limited to a value equal to orgreater than zero and equal to or less than one. In other words, α mayhave a value which is less than zero or greater than one. Accordingly,based on Equations 12 through 19, an odd-number-tap interpolation filterhaving an odd number of filter taps may be obtained. Because the numberof filter taps is an odd number, interpolation filtering using theinterpolation filter may be performed on an odd number of referencepixels.

The interpolation filter may also be obtained by combining aninterpolation filter using reference pixels which are asymmetricallylocated with respect to an interpolation location, and an odd-number-tapinterpolation filter. That is, an interpolation filter for performinginterpolation filtering on an odd number of pixels which areasymmetrically located with respect to an interpolation location is alsoavailable.

If the center of reference pixels in Equations 12 through 15 isgeneralized, filter coefficients of an interpolation filter may beinduced according to Equations 20 and 21 below.

$\begin{matrix}{C_{k} = {\sum\limits_{l = M_{\min}}^{M_{\max}}\; {D_{lk} \cdot p_{l}}}} & \left\lbrack {{Equation}\mspace{14mu} 20} \right\rbrack \\{D_{lk} = {\frac{2}{Size} \cdot {\cos \left( \frac{\pi \cdot k \cdot \left( {{2 \cdot l} - {2 \cdot {Center}} + {Size}} \right)}{2 \cdot {Size}} \right)}}} & \left\lbrack {{Equation}\mspace{20mu} 21} \right\rbrack\end{matrix}$

Here, M_(max) and M_(min) respectively represent minimum and maximumindex values from among reference pixels, and may represent the range ofthe reference pixels. Accordingly, a filter size (i.e., “Size”) may bedetermined as M_(max)−M_(min)+1. For example, in a 7-tap interpolationfilter, if M_(max)=3 and M_(min)−3, a central index (i.e. “Center”) ofreference pixels may be equal to zero. In other words, Center has anaverage value of M_(max) and M_(min).

Also, if a basis function for an interpolation filter according toEquations 20 and 21 is represented as a basis function Wk of a cosinetransformation function, Equations 22 and 23 below are induced.

$\begin{matrix}{p_{\alpha} = {\sum\limits_{k = 0}^{{Size} - 1}\; {W_{k} \cdot C_{k}}}} & \left\lbrack {{Equation}\mspace{14mu} 22} \right\rbrack \\{{{W_{0} = \frac{1}{2}};}{{W_{k} = {\cos \left( \frac{\pi \cdot k \cdot \left( {{2 \cdot \alpha} - {2 \cdot {Center}} + {Size}} \right)}{2 \cdot {Size}} \right)}};}{1 \leq k \leq {{Size} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 23} \right\rbrack\end{matrix}$

Accordingly, the interpolation filter may be an asymmetric interpolationfilter using reference pixels asymmetrically located with respect to aninterpolation location, and may include an odd-number-tap interpolationfilter of which the number of filter coefficients is an odd number. Asdescribed above in relation to Equations 38 through 40 and 4 through 7above, the interpolation filter may also include a symmetricinterpolation filter and an even-number-tap interpolation filter.

In general, an odd-number-tap interpolation filter may be an asymmetricinterpolation filter. However, an even-number-tap interpolation filtermay be either of a symmetric interpolation filter or an asymmetricinterpolation filter. For example, an 8-tap interpolation filter may bea symmetric even-number-tap interpolation filter if it includes fourfilter coefficients and four filter coefficients on each side of aninterpolation location in a region supported by the symmetriceven-number-tap interpolation filter, and may be an asymmetriceven-number-tap interpolation filter if it includes three filtercoefficients and five filter coefficients on each respective side of aninterpolation location in a region supported the asymmetriceven-number-tap interpolation filter.

The interpolation filter may include filter coefficients generated byadjusting the smoothness of a response of the interpolation filter basedon an interpolation location.

A case in which a window filter is used to determine various smoothedinterpolation filters will now be described in detail.

Smoothed Interpolation Filter Using Window Filter

A method for smoothing interpolation filter coefficients by using awindow filter will now be described in detail.

A window filter may use any one or more of a Hamming window function, acosine window function, an exponential window function, a Hanning windowfunction, a Blackman window function, and a triangle window function.Although cases when interpolation filters based on transformation andinverse transformation are smoothed by using certain window functionswill be described below for convenience of explanation, it will beunderstood by one of ordinary skill in the art that, in addition to thedescribed window functions, other window functions having similarfrequency responses may also be used.

Window coefficients according to a Hamming window function satisfyEquation 24 below.

$\begin{matrix}{{{w(n)} = {0.54 - {0.46\mspace{14mu} {\cos \left( \frac{2\; \pi \; n}{N} \right)}}}},{0 \leq n \leq N}} & \left\lbrack {{Equation}\mspace{14mu} 24} \right\rbrack\end{matrix}$

In various window functions including the Hamming window function, aninput n is symmetric with reference to N/2 and a frequency response issimilar to that of a low pass filter. From among inputs of a windowfunction, only an input covered by a window formed by the windowfunction may be output. A window size N may be set as a positive integergreater than the length of an original interpolation filter. Forexample, in order to apply a window function to an interpolation filterfor generating a sub-pel-unit pixel such as a ½ or ¼ pixel, the centrallocation of the window function may be moved by a ½ or ¼ pixel. That is,because the central location of the window function is moved to aninterpolation location, the window function may be symmetric withrespect to the interpolation location.

For example, Equations 25 and 26 below show window coefficients ofHamming window functions for ½-pel-unit and ¼-pel-unit interpolationfilters, respectively.

$\begin{matrix}{{w_{1/2}(n)} = {0.54 - {0.46\mspace{11mu} \cos \frac{2\; \pi}{N}\left( {\frac{N - 1}{2} + n} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 25} \right\rbrack \\{{w_{1/4}(n)} = {0.54 - {0.46\mspace{11mu} \cos \frac{2\; \pi}{N}\left( {\frac{{2N} - 1}{4} + n} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 26} \right\rbrack\end{matrix}$

Equation 27 below sequentially shows window coefficients of a Hammingwindow function, a cosine window function, and an exponential windowfunction as window functions for interpolation filters, which aregeneralized according to a sub-pel-unit interpolation location α.

$\begin{matrix}{{{w_{\alpha}(n)} = {0.54 - {0.46\mspace{11mu} {\cos \left( {\frac{2\; \pi}{N}\left( {\frac{N}{2} - \alpha + m} \right)} \right)}}}}{{w_{\alpha}(n)} = {\cos \left( {\pi \frac{{m -} \propto}{N}} \right)}}{{w_{\alpha}(n)} = {\exp \left\{ {- {\beta \left( {\alpha - m} \right)}^{2}} \right\}}}} & \left\lbrack {{Equation}\mspace{14mu} 27} \right\rbrack\end{matrix}$

By combining the window coefficients according to Equation 27 with anoriginal interpolation filter f_(k)(α), smoothed interpolation filtercoefficients may be determined according to Equation 28 below.

f _(k)(α)=f _(k)(α)w _(α)(k),k=−M+1, . . . , M  [Equation 28]

Because a smoothed interpolation filter is determined by using a windowfilter, a weight of an interpolation filter coefficient may be adjustedbased on the distance between an integer-pel-unit reference pixel and aninterpolation location. For example, a smoothed interpolation filter maybe determined in such a way that, by a window function, from amongfilter coefficients of an interpolation filter, a filter coefficient foran integer-pel-unit reference pixel located far from an interpolationlocation is greatly smoothed, and a filter coefficient for aninteger-pel-unit reference pixel located close to the interpolationlocation is not greatly changed.

Further, if a smoothed interpolation filter is determined by using awindow filter, interpolation filtering may be performed afterinteger-pel-unit reference pixels are smoothed. Input integer-pel-unitreference pixels Ref={p_(−M+1), p_(−M+2), . . . , p₀, p₁, . . . , p_(M)}may include noise or may be damaged due to an error such as aquantization error. As such, if integer-pel-unit reference pixels aresmoothed before interpolation filtering is performed, the imageinterpolation apparatus 10 may improve an interpolation effect.

Interpolation Filter Using Asymmetric Window Filter

An asymmetric window filter is asymmetric with respect to the center ofthe filter. Accordingly, an asymmetric window filter for aninterpolation filter may be used to perform interpolation filteringasymmetrically with respect to an interpolation location.

Equation 29 below shows filter coefficients wl of an asymmetric windowfilter in the simplest form.

$\begin{matrix}{{{{w_{l} = {\cos \left( {\pi \frac{{l -} \propto}{N - 1}} \right)}};} - M_{\min}} \leq l \leq M_{\max}} & \left\lbrack {{Equation}\mspace{14mu} 29} \right\rbrack\end{matrix}$

N represents a window size, and M_(min) and M_(max) represent referencepixels of the furthermost locations from an interpolation location.

Filter characteristics of a window filter may be adjusted by varying thewindow size N. The window size N may be equal to or greater than afilter size “Size” of an interpolation filter, and may be equal to orless than twice the filter size Size (Size≦N≦2×Size)

For example, when Equations 38 through 40 and 4 through 7 above arecombined with Equation 29 above, if filter coefficients of a symmetricinterpolation filter in which M is 4 are determined, because the numberof reference pixels (2M) is eight, an 8-tap interpolation filter isobtained. If a window function in which the window size N=13 is used,filter coefficients of a ¼-pel-unit interpolation filter and a½-pel-unit interpolation filter are as represented below. Here, a usedscaling factor S is equal to 64.

¼-pel-unit interpolation filter coefficients {p_(l)}={−1, 4, −10, 57,19, −7, 3, −1}

½-pel-unit interpolation filter coefficients {p_(l)}={−1, 4, −11, 40,40, −11, 4, −1}

Similarly, when Equations 38 through 40 and 4 through 7 are combinedwith Equation 29, if M_(min) and M_(max) are variably adjusted, filtercoefficients of an asymmetric interpolation filter may be determined byusing an asymmetric window filter.

Smoothed Interpolation Filter Using Two Parameters

A smoothed interpolation filter may determine the smoothness of filtercoefficients based on two parameters. Sub-pel-unit smoothedinterpolation filter coefficients obtained by combining a smoothingmatrix S and interpolation filter coefficients based on transformationand inverse transformation satisfy Equation 30 below.

{tilde over (f)}(α)=f(α)^(T) ·S  [Equation 30]

Equation 31 below shows an example of the smoothing matrix S.

s _(ij)=0;

{s _(ii)=1−σ_(i) ;s _(i,i+1)=σ_(i) }; i=−M+1

{s _(ii)=1−2σ_(i) ;s _(i,i±1)=σ_(i) }; −M+1≦i≦M

{s _(ii)=1−σ_(i) ;s _(i,i−1)=σ_(i) }; i=M  [Equation 31]

The smoothing matrix S according to Equation 31 is a 3-diagonal matrix.In particular, from among components of the smoothing matrix S,components other than components on one central diagonal line and twodiagonal lines corresponding to each other and adjacent to the centraldiagonal line are all equal to zero.

In the smoothing matrix S, a smoothness σ_(i) may be determinedregardless of the distance (i−α) from integer-pel-unit pixels to beinterpolated. In this case, smoothing according to the smoothing matrixS may be referred to as uniform smoothing.

Further, in the smoothing matrix S, the smoothness a may be changedbased on an index l of an integer-pel-unit pixel location. In this case,smoothing according to the smoothing matrix S may be referred to asnon-uniform smoothing. For example, the smoothness σ_(i) may satisfyEquation 32 below.

σ_(i)=β(i−α)^(l)  [Equation 32]

A positive index l may increase a smoothing effect if the distancebetween an interpolation location and an integer-pel-unit referencepixel is large. Accordingly, the positive index l may control the speedof smoothing based on the distance between an interpolation location andan integer-pel-unit reference pixel. A smoothing parameter β may controlthe range of smoothing around an interpolation location.

If the smoothing parameter β is less than zero, the smoothing matrix Saccording to Equation 13 may be changed into a sharpening filter.Accordingly, if the smoothing matrix S that is less than zero iscombined with an interpolation filter using transformation and inversetransformation, a filter for amplifying high-frequency components may begenerated.

In order to perform sub-pel-unit prediction, the image interpolationapparatus 10 may use smoothed interpolation filter coefficient datapreviously stored in memory.

FIG. 6 is a graph 67 of a smoothing factor based on a smoothingparameter β of a smoothed interpolation filter, according to anexemplary embodiment.

First and second curves 68 and 69 show a smoothing factor for smoothingan interpolation filter based on discrete transformation. If m is large,that is, if the distance from integer-pel-unit pixels to be interpolatedis increased, the smoothing factor is close to zero.

Here, in comparison to the second curve 69 in a case when the smoothingparameter β is large, the first curve 68 in a case when the smoothingparameter β is small has a relatively large width of the smoothingfactor. In other words, if the smoothing parameter β of the smoothedinterpolation filter is large, low-frequency components may be mainlyfiltered, and thus, relatively strongly smoothed sub-pel-unit pixelvalues may be generated. If the smoothing parameter β of the smoothedinterpolation filter is relatively small, relatively high-frequencycomponents may remain and be interpolated, and thus, sub-pel-unit pixelvalues may be generated.

Various interpolation filters and filter coefficients are describedabove. In particular, as a function for determining filter coefficientsof an interpolation filter, any one or more of a window function, aspline function, a polynomial function, etc. may be used. For aninterpolation filter, a frequency response of a function may varyaccording to a frequency, but a filter gain of the frequency response ofthe function may be close to one. Accordingly, the image interpolationapparatus 10 may determine filter coefficients by using a function ofwhich a filter gain of a frequency response is closest to one, even whena frequency varies, and may select an interpolation filter including thefilter coefficients.

Regularized Interpolation Filter

If a filter size of an interpolation filter is increased, the accuracyof interpolation may be improved. However, if the filter size isincreased, high-frequency components remain in a filtering result, andthus, the interpolation filter is vulnerable to noise. The interpolationfilter may smooth reference pixel values {p_(l)} by using a cosinewindow function having an interpolation location α as its center,thereby reducing noise in an interpolation filtering result. Anoperation of smoothing the reference pixel values {p_(l)} by using acosine window function satisfies Equation 33 below.

$\begin{matrix}{p_{l\;} = {p_{l} \cdot {\cos \left( {\pi \cdot \frac{l - \alpha}{N}} \right)}}} & \left\lbrack {{Equation}\mspace{14mu} 33} \right\rbrack\end{matrix}$

N represents a window size for smoothing but may not necessarily be aninteger. Accordingly, if filtering using transformation and inversetransformation according to Equation 7 is combined with window filteringaccording to Equation 33, smoothed interpolation filtering for asub-pel-unit interpolation location α is enabled. The smoothedinterpolation filtering may be performed by using a finite impulseresponse (FIR) filter and satisfies Equations 34 and 35 below.

$\begin{matrix}{p_{\alpha} = {\sum\limits_{l = M_{\min}}^{M_{\max}}\; {{{Filter}_{l}(\alpha)} \cdot p_{l}}}} & \left\lbrack {{Equation}\mspace{14mu} 34} \right\rbrack \\{{{Filter}_{l}(\alpha)} = {{\cos \left( {\pi \cdot \frac{l - \beta}{N}} \right)} \cdot {\sum\limits_{k = 0}^{{Size} - 1}\; {{W_{k}(\alpha)} \cdot D_{lk}}}}} & \left\lbrack {{Equation}\mspace{14mu} 35} \right\rbrack\end{matrix}$

In Equations 34 and 35, p_(α) represents a pixel value generated as asmoothed interpolation filtering result, and Filter_(l)(α) representsfilter coefficients of a smoothed interpolation filter. M_(min) andM_(max) represent the range of reference pixels.

In a smoothed interpolation filter for chroma pixels, a smoothingparameter of the smoothed interpolation filter may be adjusted to moregreatly reduce the influence of high-frequency components. Filtercoefficients of a chroma interpolation filter using a smoothingparameter may be determined as represented in Equations 36 and 37 below.

$\begin{matrix}{{{\overset{\sim}{W}}_{k} = \frac{W_{k}(\alpha)}{1 + {\sigma \cdot k^{2}}}},{1 \leq k \leq {{Size} - 1}}} & \left\lbrack {{Equation}\mspace{14mu} 36} \right\rbrack \\{{{Filter}_{l}(\alpha)} = {\sum\limits_{k = 0}^{{Size} - 1}\; {{{\overset{\sim}{W}}_{k}(\alpha)} \cdot D_{lk}}}} & \left\lbrack {{Equation}\mspace{14mu} 37} \right\rbrack\end{matrix}$

FIG. 7 is an amplitude frequency response graph 70 of interpolationfilters, according to an exemplary embodiment.

If a harmonic signal having a size of one is input to the interpolationfilters, the amplitude frequency response graph 70 of the interpolationfilters may show results of performing interpolation filtering.

The amplitude frequency response graph 70 shows a first frequencyresponse 71 of an 8-tap smoothed interpolation filter using DCT and IDCTbased on basis functions, according to an exemplary embodiment, a secondfrequency response 72 of a regularized 8-tap smoothed interpolationfilter according to an exemplary embodiment, and a third frequencyresponse 73 of a 6-tap interpolation filter according to the H.264 videocoding standard.

In the first, second, and third frequency responses 71, 72, and 73,hills 711, 715, 721, and 731 represent that signals are amplified atcorresponding frequencies, and a valley 713 represents that a signal isdamped at a corresponding frequency. An effect that an input signal isamplified or damped is not appropriate in interpolation filtering.

In an ideal amplitude frequency response 74, a filter gain is constantlymaintained as 1.0 at all frequencies, and thus a hill or valley does notexist at all. This means that distortion due to interpolation filteringdoes not occur.

If a frequency response of an interpolation filter is closer to theideal amplitude frequency response 74, an interpolation filtering resultis more accurate. Distortion in a frequency response of an interpolationfilter in comparison to the ideal amplitude frequency response 74 may berepresented as a square of the difference between the frequency responseof the interpolation filter and the ideal amplitude frequency response74, i.e., an area of a difference region.

For example, distortion in a frequency response of the regularizedsmoothed interpolation filter in comparison to the ideal amplitudefrequency response 74 may be minimized by adjusting its window filtersize N and its smoothness a. The distortion in the frequency response ofthe regularized smoothed interpolation filter in comparison to the idealamplitude frequency response 74 corresponds to an area of a shadedregion between the ideal amplitude frequency response 74 and the secondfrequency response 72 in the amplitude frequency response graph 70. Inparticular, if the area of the shaded region is small, the accuracy ofinterpolation performed by using the regularized smoothed interpolationfilter may be improved.

Further, because a frequency response of an FIR filter is close to zeroas a frequency is close to Tr, the FIR filter may not generatehigh-frequency components. In addition, if a cut level of aninterpolation filter is low, the interpolation filter may not restoredetailed information of a reference image. In general, if the length ofa filter is large, a high cut level may be assigned. In the amplitudefrequency response graph 70, because cut levels 719 and 729 of the firstand second frequency responses 71 and 72 of the smoothed interpolationfilter and the regularized smoothed interpolation filter are higher thana cut level 739 of the third frequency response 73 of the H.264interpolation filter, the smoothed interpolation filter and theregularized smoothed interpolation filter may restore detailedinformation of a reference image more accurately in comparison to theH.264 interpolation filter.

Accordingly, in comparison to the H.264 interpolation filter, thesmoothed interpolation filter may leave high-frequency components of aninput signal after performing interpolation filtering. Further, incomparison to the H.264 interpolation filter, a distortion region of thesmoothed interpolation filter is relatively small, and thus, distortionin an interpolation result is relatively small.

From among smoothed interpolation filters, the second frequency response72 of the regularized smoothed interpolation filter is relatively closeto the ideal amplitude frequency response 74, and the first frequencyresponse 71 of the unregularized smoothed interpolation filter has arelatively large distortion region due to hills and valleys. In otherwords, in comparison to the regularized smoothed interpolation filter, afiltering result of the unregularized smoothed interpolation filter mayinclude more undesired artifacts.

Accordingly, as filter coefficients of an interpolation filter accordingto an exemplary embodiment, filter coefficients of the regularizedsmoothed interpolation filter for minimizing a distortion region incomparison to the ideal amplitude frequency response 74 may be selected.In other words, if the window filter size N and the smoothness σ of thesmoothed interpolation filter are adjusted and its filter coefficientsare regularized, filter coefficients for minimizing a distortion regionof a frequency response of the smoothed interpolation filter may bedetermined.

Therefore, interpolation filters of the image interpolation apparatus 10may include filter coefficients which are determined in consideration ofsmoothing.

Phase Shift α & Motion Vector Value

The accuracy for typical motion compensation is in a sub-pel unit of a½^(p)-pel unit, such as, for example, a ½-pel unit or a ¼-pel unit.However, an interpolation location α for determining filter coefficientsof a sub-pel-unit interpolation filter according to an exemplaryembodiment is not limited to a ½^(p)-pel unit.

In order to perform motion compensation on the interpolation location αin a sub-pel unit other than a ½-pel unit or a ¼-pel unit, partialvectors of a ½-pel-unit or ¼-pel-unit motion vector may be used. Forexample, a sub-pel-unit component set {α, ½, 1−α} of a ½-pel-unit motionvector MV is assumed. Because the length of coding unit components ofthe motion vector MV is reduced if α is less than ¼, the stability ofinterpolation filtering for motion compensation may be improved andcoding bits for a differential motion vector may be saved.

The most commonly used color format in video coding is a 4:2:0 format.In this case, chroma samples corresponding to a half of the number ofluma samples may be encoded. If the same motion vector is shared betweenthe luma and chroma samples, the size of a chroma motion vector is ahalf of the size of a luma motion vector. Accordingly, a phase shift ofa luma interpolation filter may be synchronized with the phase shift ofa chroma interpolation filter.

For example, if the phase shift of the luma interpolation filter is{α_(i)}, the phase shift of the chroma interpolation filter may besynchronized to {α_(i)/2}∪{1−α_(i)/2}∪{½}.

For example, when motion compensation is performed by using thesub-pel-unit component set of the motion vector MV, if the phase shiftof the luma interpolation filter is {α, ½, 1−α}, the phase shift of thechroma interpolation filter may be synchronized to {α/2, (1−α)/2, ½,1−α/2, 1−(1−α)/2}.

As interpolation filters according to exemplary embodiments, aninterpolation filter using transformation and inverse transformationbased on a plurality of basis functions, an interpolation filter forperforming interpolation in a sub-pel unit, a symmetric interpolationfilter and an asymmetric interpolation filter, an odd- oreven-number-tap interpolation filter, an interpolation filter using awindow filter, an interpolation filter considering smoothing, and aregularized interpolation filter are described above.

The above-mentioned interpolation filters may operate individually ormay be combined. For example, an interpolation filter according to anexemplary embodiment may perform interpolation in a sub-pel unit and mayperform interpolation filtering regardless of whether reference pixelsare symmetrically or asymmetrically located with respect to aninterpolation location. IN addition, because the number of filtercoefficients may be an even or odd number, the interpolation filter mayperform interpolation filtering on an odd number of integer-pel-unitpixels and/or an even number of integer-pel-unit pixels. Furthermore,because filter coefficients of a regularized smoothed interpolationfilter may be selected, detailed information of reference pixels mayremain and undesired high-frequency components such as noise may beminimized, thereby minimizing distortion due to interpolation filtering.

FIG. 8 is a flowchart which illustrates an image interpolation method,according to an exemplary embodiment.

In operation 81, from among a plurality of interpolation filters whichare configured for generating at least one sub-pel-unit pixel valuelocated between integer-pel units of a picture, one of a symmetricinterpolation filter and an asymmetric interpolation filter isindividually selected based on a sub-pel-unit interpolation location.

The selected asymmetric interpolation filter may be an odd-number-tapinterpolation filter. The selected symmetric interpolation filter may bean even-number-tap interpolation filter. In order to interpolateinteger-pel-unit pixels in a spatial domain, the interpolation filtermay include filter coefficients obtained by combining a filter usingtransformation and inverse transformation based on a plurality of basisfunctions with an asymmetric window filter or a symmetric window filter.

An interpolation filter which is regularized in order to minimize afrequency response error generated as an interpolation result when usingthe selected interpolation filter is selected. Also, in order to preventhigh-frequency components such as noise from being restored, aninterpolation filter which includes filter coefficients for smoothingreference pixels may be selected.

In operation 83, integer-pel-unit pixel values are interpolated by usingthe interpolation filter selected in operation 81, thereby generating atleast one sub-pel-unit pixel value.

If an asymmetric interpolation filter is selected in operation 81, inoperation 83, filtering may be performed on integer-pel-unit pixelswhich are asymmetrically located with respect to an interpolationlocation. If a symmetric interpolation filter is selected in operation81, in operation 83, filtering may be performed on integer-pel-unitpixels which are symmetrically located with respect to an interpolationlocation.

Further, if an asymmetric odd-number-tap interpolation filter isselected in operation 81, in operation 83, filtering may be performed onan odd number of integer-pel-unit pixels located with respect to aninterpolation location by using an odd number of filter coefficients ofthe asymmetric odd-number-tap interpolation filter. If a symmetriceven-number-tap interpolation filter is selected in operation 81, inoperation 83, filtering may be performed on an even number ofinteger-pel-unit pixels located with respect to an interpolationlocation by using an even number of filter coefficients of the symmetriceven-number-tap interpolation filter.

Various examples of respective filter coefficients of a symmetricinterpolation filter and an asymmetric interpolation filter which isselectively determined based on a sub-pel-unit interpolation locationwill now be described with reference to FIGS. 9A through 12B.

According to the above-described principles, the interpolation filterillustrated in FIGS. 9A through 12B is a filter obtained by combining asub-pel-unit interpolation filter using transformation and inversetransformation based on a plurality of basis functions with a windowfilter for smoothing high-frequency components, and includes filtercoefficients of which a window size and a smoothness are adjusted tominimize distortion in an interpolation result. Also, various symmetricand asymmetric interpolation filters and odd- and even-number-tapinterpolation filters will be described below.

Because the interpolation filter is a mirror-reflective symmetricfilter, a filter coefficient f_(m)(1−α) of an interpolation location(1−α) may be determined by using a filter coefficient f_(m)(α) of aninterpolation location α. Accordingly, in the tables shown in FIGS. 9Athrough 12B, although only interpolation filter coefficients {f_(m)(α)}in a case when a sub-pel unit of a motion vector MV is equal to or lessthan ½ are shown, it will be understood by one of ordinary skill in theart that other interpolation filter coefficients {f_(m)(α)} in a casewhen the sub-pel unit of the motion vector MV is greater than ½ may bedetermined.

Initially, in the tables shown in FIGS. 9A through 11C, ‘FracMV’ in thefirst column represents a sub-pel unit of a motion vector MV for½^(p)-pel-unit motion compensation. In order to perform sub-pel-unitinterpolation filtering, a value of ‘FracMV’ may be combined with filtercoefficients in the second column. An interpolation location α in thethird column is a parameter for defining a sub-pel-unit interpolationlocation and may represent a phase shift amount from an integer-pelunit. A window filter size N in the fourth column may not necessarily bean integer. Scaling bits of the interpolation filter is 6 bits.

FIGS. 9A, 9B, 9C, and 9D respectively show filter coefficients of 3-tapthrough 6-tap interpolation filters which are determined based on aninterpolation location and a window filter size, according to exemplaryembodiments.

FIG. 9A shows an asymmetric interpolation filter that is a 3-tapinterpolation filter and includes filter coefficients {p⁻¹, p₀, p₁}.Accordingly, the interpolation filter shown in FIG. 9A may performinterpolation filtering on integer-pel-unit pixels which areasymmetrically located with respect to an interpolation location. Forexample, if horizontal interpolation is performed, interpolationfiltering may be performed on two left integer-pel-unit reference pixelsand one right integer-pel-unit reference pixel with respect to aninterpolation location.

FIG. 9B shows a symmetric interpolation filter that is a 4-tapinterpolation filter and includes filter coefficients {p⁻¹, p₀, p₁, p₂}.Accordingly, the interpolation filter shown in FIG. 9B may performinterpolation filtering on integer-pel-unit pixels which aresymmetrically located with respect to an interpolation location. Forexample, if horizontal interpolation is performed, interpolationfiltering may be performed by using two left integer-pel-unit referencepixels and two right integer-pel-unit reference pixels with respect toan interpolation location.

FIG. 9C shows an asymmetric interpolation filter that is a 5-tapinterpolation filter and includes filter coefficients {p⁻¹, p₀, p₁, p₂,p₃}. Accordingly, if horizontal interpolation is performed,interpolation filtering may be performed on two left integer-pel-unitreference pixels and three right integer-pel-unit reference pixels whichare asymmetrically located with respect to an interpolation location.

FIG. 9D shows a symmetric interpolation filter that is a 6-tapinterpolation filter and includes filter coefficients {p⁻², p⁻¹, p₀, p₁,p₂, p₃}. Accordingly, if horizontal interpolation is performed,interpolation filtering may be performed by using three leftinteger-pel-unit reference pixels and three right integer-pel-unitreference pixels which are symmetrically located with respect to aninterpolation location.

FIGS. 10A, 10B, and 10C respectively show filter coefficients of 7-tapinterpolation filters which are determined based on an interpolationlocation and a window filter size, according to exemplary embodiments.

FIG. 10A shows an asymmetric interpolation filter including filtercoefficients {p⁻³, p⁻², p⁻¹, p₀, p₁, p₂, p₃}. Accordingly, if horizontalinterpolation is performed by using the interpolation filter shown inFIG. 10A, interpolation filtering may be performed on four leftinteger-pel-unit reference pixels and three right integer-pel-unitreference pixels which are asymmetrically located with respect to aninterpolation location.

FIG. 10B shows an asymmetric interpolation filter including filtercoefficients {p⁻², p⁻¹, p₀, p₁, p₂, p₃, p₄}. Accordingly, if horizontalinterpolation is performed by using the interpolation filter shown inFIG. 10B, interpolation filtering may be performed on three leftinteger-pel-unit reference pixels and four right integer-pel-unitreference pixels which are asymmetrically located with respect to aninterpolation location.

FIG. 10C shows an asymmetric interpolation filter including filtercoefficients {p⁻¹, p₀, p₁, p₂, p₃, p₄, p₅}. Accordingly, if horizontalinterpolation is performed by using the interpolation filter shown inFIG. 10C, interpolation filtering may be performed on two leftinteger-pel-unit reference pixels and five right integer-pel-unitreference pixels which are asymmetrically located with respect to aninterpolation location.

FIGS. 11A, 11B, and 11C respectively show filter coefficients of 8-tapinterpolation filters which are determined based on an interpolationlocation and a window filter size, according to exemplary embodiments.

FIG. 11A shows a symmetric interpolation filter including filtercoefficients {p⁻³, p⁻², p⁻¹, p₀, p₁, p₂, p₃, p₄}. Accordingly, ifhorizontal interpolation is performed by using the interpolation filtershown in FIG. 11A, interpolation filtering may be performed on four leftinteger-pel-unit reference pixels and four right integer-pel-unitreference pixels which are symmetrically located with respect to aninterpolation location.

FIG. 11B shows an asymmetric interpolation filter including filtercoefficients {p⁻², p⁻¹, p₀, p₁, p₂, p₃, p₄, p₅}. Accordingly, ifhorizontal interpolation is performed by using the interpolation filtershown in FIG. 11B, interpolation filtering may be performed on threeleft integer-pel-unit reference pixels and five right integer-pel-unitreference pixels which are asymmetrically located with respect to aninterpolation location.

FIG. 11C shows an asymmetric interpolation filter including filtercoefficients {p⁻⁴, p⁻³, p⁻², p⁻¹, p₀, p₁, p₂, p₃}. Accordingly, ifhorizontal interpolation is performed by using the interpolation filtershown in FIG. 11C, interpolation filtering may be performed on five leftinteger-pel-unit reference pixels and three right integer-pel-unitreference pixels which are asymmetrically located with respect to aninterpolation location.

FIGS. 12A and 12B respectively show filter coefficients of a regularizedluma interpolation filter and a regularized chroma interpolation filter,according to exemplary embodiments.

FIGS. 12A and 12B show filter coefficients of regularized interpolationfilters selected to minimize a distortion region as described above inthe “Regularized Interpolation Filter” section.

According to FIG. 12A, a window filter size N is adjusted in order toregularize a luma interpolation filter. From among various interpolationfilters shown in FIG. 9A through 11C, a 7-tap interpolation filter {−1,4, −10, 58, 17, −5, −1} having a window size of 8.7 may be selected as aregularized luma interpolation filter for performing ¼-pel-unitinterpolation filtering. In addition, an 8-tap interpolation filter {−1,4, −11, 40, 40, −11, 4, −1} having a window size of 9.5 may be selectedas a regularized luma interpolation filter for performing ½-pel-unitinterpolation filtering. In particular, an asymmetric interpolationfilter may be selected as a regularized ¼-pel-unit luma interpolationfilter, and a symmetric interpolation filter may be selected as aregularized ½-pel-unit luma interpolation filter.

According to FIG. 12B, a smoothness σ is adjusted in order to regularizea chroma interpolation filter. A ⅛-pel-unit 4-tap symmetricinterpolation filter may be selected as a regularized chromainterpolation filter.

Video encoding and decoding using an interpolation filter, according toexemplary embodiments, are described below with reference to FIGS. 13Athrough 27. Video encoding and decoding based on coding units having atree structure, according to exemplary embodiments, are described belowwith reference to FIGS. 15 through 25. Video encoding and decodingmethods using an interpolation filter, according to exemplaryembodiments, are described below with reference to FIGS. 26 and 27.

When various operations are performed on image data, the image data maybe split into data groups, and the same operation may be performed ondata of the same data group. In the following description, a data groupformed according to a predetermined standard is referred to as a ‘dataunit’, and an operation is performed on each ‘data unit’ by using dataincluded in the data unit.

Video Encoding and Decoding Using Interpolation Filter

FIG. 13A is a block diagram of a video encoding apparatus 100 which usesan interpolation filter, according to an exemplary embodiment.

Operations of an encoder 120 and an output unit (also referred to hereinas an “output component”) 130 of the video encoding apparatus 100 may becooperatively controlled by any one or more of a video encodingprocessor, a CPU, and a graphic processor.

In order to encode a current picture of an input video, the videoencoding apparatus 100 splits the current picture into data units havinga predetermined size and encodes each data unit.

For example, the current picture may include pixels in a spatial domain.In order to encode spatially adjacent pixels of the current picture atthe same time, the current picture may be split into pixel groups havinga predetermined size in such a way that adjacent pixels within apredetermined range form one group. By performing a series of encodingoperations on pixels of the split pixel groups, the current picture maybe encoded.

Because initial data of a picture to be encoded are pixel values in thespatial domain, each pixel group may be used as a data unit to beencoded. Further, when transformation coefficients in a transformationdomain are generated by performing transformation for video encoding onpixel values of the pixel group in the spatial domain, thetransformation coefficients are included in coefficient groups havingthe same size as the pixel groups in the spatial domain. Accordingly, acoefficient group of the transformation coefficients in thetransformation domain may also be used as a data unit for encoding apicture.

Accordingly, in the spatial domain and the transformation domain, a datagroup having a predetermined size may be used as a data unit to beencoded. In this case, the size of a data unit may be defined as thenumber of pieces of data included in the data unit. For example, thenumber of pixels in the spatial domain or the number of transformationcoefficients in the transformation domain may represent the size of adata unit.

An encoding method or encoding characteristics of a current data unitmay be determined with respect to each data group of any data level fromamong a data unit, a slice, a picture, and a picture sequence of a videoto be currently encoded.

The video encoding apparatus 100 may encode the current picture byperforming prediction encoding including any one or more of interprediction and intra prediction, transformation, quantization, andentropy encoding on each data unit.

According to inter prediction, in order to estimate a current pixelvalue with reference to a pixel value of a temporally previous orsubsequent picture, residual data between a pixel value of a referenceregion of a reference picture and a pixel value of a current picture,and reference data indicating the referred to pixel value may bedetermined.

In order to more accurately perform inter prediction, the video encodingapparatus 100 may determine the residual data and the reference data byusing a sub-pel-unit pixel value. In order to perform sub-pel-unit interprediction, the video encoding apparatus 100 may determine asub-pel-unit pixel value located between adjacent integer-pel-unitpixels by interpolating the adjacent integer-pel-unit pixels.

Further, the sub-pel-unit pixel value may be generated by performinginterpolation filtering on two or more integer-pel-unit referencepixels, including the adjacent integer-pel-unit pixels. The referencepixels for performing interpolation filtering may include pixels of areference picture.

In order to efficiently perform image interpolation, the video encodingapparatus 100 may selectively determine interpolation filtercoefficients. The encoder 120 may include the image interpolationapparatus 10 illustrated in FIG. 1. In particular, in order to performsub-pel-unit inter prediction, the encoder 120 may generate asub-pel-unit pixel value by using an interpolation filter includingfilter coefficients determined by the image interpolation apparatus 10based on transformation and inverse transformation.

In order to efficiently perform interpolation filtering, the videoencoding apparatus 100 may previously store interpolation filtercoefficients in memory. According to an interpolation location, asmoothness, the number of filter taps, a bit depth, a scaling ratio, abasis function of interpolation filtering based on transformation, awindow function, and a window size, various interpolation filtercoefficients may be stored in memory of the video encoding apparatus100.

For example, i) a ¼-pel-unit interpolation filter including 7-tap filtercoefficients {−1, 4, −10, 58, 17, −5, 1} and having a window size of8.7, and ii) a ½-pel-unit interpolation filter including 8-tap filtercoefficients {−1, 4, −11, 40, 40, −11, 4, −1} and having a window sizeof 9.5 may be stored in memory, and may be used to perform interpolationfiltering.

In addition to the above-mentioned interpolation filter coefficients,interpolation filter coefficients which are modifiable according tovarious basis functions and window functions as shown in FIGS. 9Athrough 12B may be used to perform interpolation filtering.

If interpolation filtering is performed by using the filter coefficientsstored in memory, a calculation speed of inter prediction may beimproved.

From among a plurality of interpolation filters, the encoder 120 mayselect and use a symmetric interpolation filter or an asymmetricinterpolation filter to perform inter prediction based on a sub-pel-unitinterpolation location α. In addition, an interpolation filter which isappropriate for a current pixel may be determined based on any one ormore of the number of filter taps, a bit depth, a scaling ratio, awindow filter size, a smoothness, etc.

The encoder 120 may determine an interpolation filter based on imagecharacteristics. For example, the encoder 120 may determine differentinterpolation filters based on respective color components of pixels.For example, an interpolation filter for luma pixels and aninterpolation filter for chroma pixels may be separately selected, andthus, sub-pel-unit pixel values may be individually generated byperforming interpolation filtering.

A video may be encoded by performing inter prediction based on any oneor more of sub-pel-unit interpolation, intra prediction, transformation,and quantization.

The output unit 130 may encode and output encoding information and mayoutput encoded picture data. As the encoding information, informationwhich relates to the selected interpolation filter may be additionallyencoded. In particular, information about an interpolation filter whichis used to perform sub-pel-unit prediction encoding may be encoded. Forexample, a decoder must know about an interpolation filter used toencode an image in order to decode the image by using the sameinterpolation filter used in the encoding process. For this, informationindicating the used interpolation filter may be encoded together withthe image. However, if a filter is selected based on a previous encodingresult, i.e., context, information about the selected filter may not beadditionally encoded.

The output unit 130 may perform entropy encoding on encoding informationand encoded picture data, and may output a bitstream.

FIG. 13B is a block diagram of a video decoding apparatus 200 which usesan interpolation filter, according to an exemplary embodiment.

The video decoding apparatus 200 includes a receiver and extractor 220and a decoder 230. Operations of the receiver and extractor 220 and thedecoder 230 of the video decoding apparatus 200 may be cooperativelycontrolled by any one or more of a video decoding processor, a graphicprocessor, and a CPU.

In order to restore an image from a bitstream, the video decodingapparatus 200 may decode encoded picture data of the bitstream byperforming operations including any one or more of entropy decoding,inverse quantization, inverse transformation, interprediction/compensation, and intra prediction/compensation.

The receiver and extractor 220 receives and parses a bitstream of anencoded video. The receiver and extractor 220 may extract encoded dataof each data unit of a current picture, and encoding information whichincludes information about an encoding method to be used to decode theencoded data, from the parsed bitstream.

If the encoding information includes interpolation filter information,the decoder 230 may read information about an interpolation filter whichhas been used to perform sub-pel-unit intra prediction from theinterpolation filter information, and may perform motion compensation byusing the interpolation filter used in an encoding process.

The decoder 230 may decode encoded picture data by performing variousdecoding operations such as any one or more of entropy decoding, inversequantization, inverse transformation, inter prediction/compensation, andintra prediction/compensation on an encoded picture according to variousdecoding methods which are determined based on information about acoding mode.

In order to perform motion compensation, a reference region of areference picture that is temporally previous or subsequent to a currentpicture may be determined by using reference data, and a pixel value ofthe reference region and residual data may be combined in order torestore a current pixel value.

If the residual data and the reference data are determined based onpixels interpolated in a sub-pel unit in an encoding process, thedecoder 230 may also perform motion compensation based on pixelsinterpolated in a sub-pel unit. In order to perform sub-pel-unit motioncompensation, the decoder 230 may generate a sub-pel-unit pixel value byinterpolating adjacent integer-pel-unit pixels of the reference picture.The sub-pel-unit pixel value may be generated by performinginterpolation filtering on two or more integer-pel-unit reference pixelsincluding the adjacent integer-pel-unit pixels.

In order to efficiently perform image interpolation, the video decodingapparatus 200 may selectively determine interpolation filtercoefficients. The decoder 230 may include the image interpolationapparatus 10 illustrated in FIG. 1. In particular, in order to performsub-pel-unit motion compensation, the decoder 230 may generate asub-pel-unit pixel value by using an interpolation filter based ontransformation.

In order to efficiently perform interpolation filtering, the videodecoding apparatus 200 may previously store variously selectableinterpolation filter coefficients in memory based on any one or more ofan interpolation location, a smoothness, the number of filter taps, abit depth, a scaling ratio, and a basis function of interpolationfiltering based on transformation.

As described above, for example, at least one of i) a ¼-pel-unitinterpolation filter including 7-tap filter coefficients {−1, 4, −10,58, 17, −5, 1} and having a window size of 8.7, and ii) a ½-pel-unitinterpolation filter including 8-tap filter coefficients {−1, 4, −11,40, 40, −11, 4, −1} and having a window size of 9.5 may be stored inmemory and may be used to perform interpolation filtering. In additionto the above-mentioned interpolation filter coefficients, interpolationfilter coefficients which are modifiable based on any one or more ofvarious basis functions and window functions as shown in FIGS. 9Athrough 12B may be used to perform interpolation filtering.

From among a plurality of interpolation filters, the decoder 230 mayselect and use an interpolation filter which is appropriate for acurrent pixel in order to perform sub-pel-unit motion compensation basedon any one or more of a sub-pel-unit interpolation location α, thenumber of filter taps, a bit depth, a scaling ratio, etc.

Further, the decoder 230 may determine an interpolation filter based onimage characteristics. For example, different interpolation filters maybe determined based on color components of pixels, interpolationfiltering for luma pixels and interpolation filtering for chroma pixelsmay be separately performed, and thus interpolated sub-pel-unit pixelvalues may be individually generated.

Accordingly, the decoder 230 may restore data in a spatial domain byperforming inverse quantization/inverse transformation, and may restorepixel values and a current picture by performing intra prediction andmotion compensation based on sub-pel-unit interpolation and/or byperforming integer-pel-unit interpolation. If pictures are restored, avideo may be decoded.

FIG. 14A is a flowchart which illustrates an image encoding method usingan interpolation filter, according to an exemplary embodiment.

In operation 1410, in order to encode a current picture of an inputvideo, prediction encoding using sub-pel-unit interpolation isperformed. From among a plurality of interpolation filters which areconfigured for generating a sub-pel-unit pixel value, an interpolationfilter is variably selected based on a sub-pel-unit interpolationlocation and a smoothness. The smoothness of the interpolation filtermay be determined based on the distance between an interpolationlocation and integer-pel units.

The sub-pel-unit pixel value may be generated by performinginterpolation filtering on two or more integer-pel-unit reference pixelsof a reference picture. Residual data and reference data are determinedby using the generated sub-pel-unit pixel value, thereby performingprediction encoding.

In order to efficiently perform image interpolation, interpolationfilter coefficients may be selectively determined. Memory may storeinterpolation filter coefficients of symmetric and asymmetricinterpolation filters, odd- and even-number-tap interpolation filters,and regularized interpolation filters. From among the interpolationfilter coefficients previously stored in memory, a desired interpolationfilter may be selected based on any one or more of a sub-pel-unitinterpolation location, a smoothness, the number of filter taps, a bitdepth, a scaling ratio, a basis function of interpolation filteringbased on transformation, a window filter size, and a color component,and interpolation may be performed in order to generate the sub-pel-unitpixel value.

In operation 1420, transformation and quantization are performed on aninter prediction result based on sub-pel-unit interpolation, and intraprediction.

In operation 1430, a bitstream may be output by performing entropyencoding on encoding information and encoded picture data in the form ofquantized transformation coefficients. The encoding information mayinclude information about an interpolation filter used to performsub-pel-unit prediction encoding.

FIG. 14B is a flowchart which illustrates an image decoding method usingan interpolation filter, according to an exemplary embodiment.

In operation 1450, a bitstream of an encoded video is received,entropy-decoded, and parsed in order to extract quantized transformationcoefficients and encoding information of a current picture from thebitstream.

If the encoding information includes information about an interpolationfilter, the type of a required interpolation filter may be read from theinformation.

In operation 1460, based on any one or more of various decoding methodswhich are determined based on a coding mode read from the encodinginformation, inverse quantization and inverse transformation areperformed on the quantized transformation coefficients, and residualdata is added, thereby restoring data in a spatial domain.

In operation 1470, encoded picture data may be decoded by performing anyone or more of various decoding operations such as motion compensationand intra prediction based on the coding mode.

In particular, if encoded residual data and reference data are extractedbased on pixels interpolated in a sub-pel unit, motion compensation maybe performed based on the pixels interpolated in a sub-pel unit. Fromamong a plurality of interpolation filters which are configured forgenerating a sub-pel-unit pixel value, an interpolation filter isvariably selected based on a sub-pel-unit interpolation location and asmoothness.

In order to efficiently perform image interpolation, interpolationfilter coefficients may be selectively determined. Memory may storerespective interpolation filter coefficients of symmetric interpolationfilters and asymmetric interpolation filters, odd- and even-number-tapinterpolation filters, and regularized interpolation filters. From amongthe interpolation filter coefficients previously stored in memory, adesired interpolation filter may be selected based on any one or more ofa sub-pel-unit interpolation location, a smoothness, the number offilter taps, a bit depth, a scaling ratio, a basis function ofinterpolation filtering based on transformation, a window filter size,and a color component, and interpolation may be performed in order togenerate the sub-pel-unit pixel value.

Because motion compensation is performed on pixels which areinterpolated by using the interpolation filter coefficients previouslystored in memory, a calculation speed may be increased. Memory may storesymmetric and asymmetric interpolation filters, and odd- andeven-number-tap interpolation filters.

A reference picture and a reference region are determined by using thereference data, and the sub-pel-unit pixel value may be generated byperforming interpolation filtering on two or more integer-pel-unitreference pixels of the reference picture. Motion compensation may beperformed by combining the generated sub-pel-unit pixel value with theresidual data, and thus prediction decoding may be performed.

In operation 1480, a current picture is restored by using pixel valuesobtained by performing prediction decoding, and thus a video is decoded.

Video Encoding and Decoding Using Interpolation Based on Coding UnitsHaving Tree Structure

Video encoding and decoding apparatuses which use an interpolationfilter based on coding units having a tree structure, and video encodingand decoding methods corresponding to the video encoding and decodingapparatuses, according to exemplary embodiments, will now be describedin detail with reference to FIGS. 13 through 27.

The video encoding apparatus 100 may encode a video based on codingunits and transformation units having a tree structure.

A current picture of a video may be split based on a maximum coding unitfor the current picture. If the current picture is larger than themaximum coding unit, image data of the current picture may be split intoat least one maximum coding unit. The maximum coding unit may be a dataunit having a size of, for example, any one of 32×32, 64×64, 128×128,256×256, etc., wherein a shape of the data unit is a square having awidth and length in squares of 2. The encoder 120 may encode picturedata of each of at least one maximum coding unit.

A coding unit according to an exemplary embodiment may be characterizedby a maximum size and a depth. The depth denotes a number of times thecoding unit is spatially split from the maximum coding unit, and as thedepth deepens, deeper coding units according to depths may be split fromthe maximum coding unit to a minimum coding unit. A depth of the maximumcoding unit is an uppermost depth and a depth of the minimum coding unitis a lowermost depth. Because a size of a coding unit corresponding toeach depth decreases as the depth of the maximum coding unit deepens, acoding unit corresponding to an upper depth may include a plurality ofcoding units corresponding to lower depths.

As described above, the image data of the current picture is split intothe maximum coding units based on a maximum size of the coding unit, andeach of the maximum coding units may include deeper coding units thatare split according to depths. Because the maximum coding unit accordingto an exemplary embodiment is split according to depths, the image dataof a spatial domain included in the maximum coding unit may behierarchically classified according to depths.

A maximum depth and a maximum size of a coding unit, which limit thetotal number of times a height and a width of the maximum coding unitare hierarchically split, may be predetermined.

The encoder 120 encodes at least one split region obtained by splittinga region of the maximum coding unit according to depths, and determinesa depth to output finally encoded image data according to the at leastone split region. In particular, the encoder 120 determines a codeddepth by encoding the image data in the deeper coding units according todepths, based on the maximum coding unit of the current picture, andselecting a depth having the least encoding error.

The encoder 120 may output the encoded image data of the coding unitcorresponding to the determined coded depth. Further, the encoder 120may transmit information about the determined coded depth to the outputunit 130 such that the information about the coded depth may be encodedas encoding information.

The image data in the maximum coding unit is encoded based on the deepercoding units corresponding to at least one depth equal to or below themaximum depth, and results of encoding the image data are compared basedon each of the deeper coding units. A depth having the least encodingerror may be selected after comparing encoding errors of the deepercoding units. At least one coded depth may be selected for each maximumcoding unit.

The size of the maximum coding unit is split as a coding unit ishierarchically split according to depths, and as the number of codingunits increases. Also, even if coding units correspond to the same depthin one maximum coding unit, it is determined whether to split each ofthe coding units corresponding to the same depth to a lower depth bymeasuring an encoding error of the image data of each coding unit,separately. Accordingly, even when image data is included in one maximumcoding unit, the image data is split into regions according to thedepths and the encoding errors may differ according to regions in theone maximum coding unit, and thus the coded depths may differ accordingto regions in the image data. Thus, one or more coded depths may bedetermined in one maximum coding unit, and the image data of the maximumcoding unit may be divided according to coding units of at least onecoded depth.

Accordingly, the encoder 120 may determine coding units having a treestructure included in the maximum coding unit. The ‘coding units havinga tree structure’ according to an exemplary embodiment include codingunits corresponding to a depth determined to be the coded depth, fromamong all deeper coding units included in the maximum coding unit. Acoding unit of a coded depth may be hierarchically determined accordingto depths in the same region of the maximum coding unit, and may beindependently determined in different regions. Similarly, a coded depthin a current region may be independently determined from a coded depthin another region.

A maximum depth according to an exemplary embodiment is an index relatedto the number of times splitting is performed from a maximum coding unitto a minimum coding unit. A first maximum depth according to anexemplary embodiment may denote the total number of times splitting isperformed from the maximum coding unit to the minimum coding unit. Asecond maximum depth according to an exemplary embodiment may denote thetotal number of depth levels from the maximum coding unit to the minimumcoding unit. For example, when a depth of the maximum coding unit is 0,a depth of a coding unit, in which the maximum coding unit is splitonce, may be set to 1, and a depth of a coding unit, in which themaximum coding unit is split twice, may be set to 2. Here, if theminimum coding unit is a coding unit in which the maximum coding unit issplit four times, 5 depth levels of depths 0, 1, 2, 3 and 4 exist, andthus the first maximum depth may be set to 4, and the second maximumdepth may be set to 5.

Prediction encoding and transformation may be performed according to themaximum coding unit. The prediction encoding and the transformation arealso performed based on the deeper coding units according to a depthequal to or depths less than the maximum depth, according to the maximumcoding unit.

Since the number of deeper coding units increases whenever the maximumcoding unit is split according to depths, encoding including theprediction encoding and the transformation is performed on all of thedeeper coding units generated as the depth deepens. For convenience ofdescription, the prediction encoding and the transformation will now bedescribed based on a coding unit of a current depth, in a maximum codingunit.

The video encoding apparatus 100 may variously select a size or shape ofa data unit for encoding the image data. In order to encode the imagedata, operations, such as prediction encoding, transformation, andentropy encoding, are performed, and at this time, the same data unitmay be used for all operations or different data units may be used foreach operation.

For example, the video encoding apparatus 100 may select not only acoding unit for encoding the image data, but also a data unit differentfrom the coding unit so as to perform the prediction encoding on theimage data in the coding unit.

In order to perform prediction encoding in the maximum coding unit, theprediction encoding may be performed based on a coding unitcorresponding to a coded depth, i.e., based on a coding unit that is nolonger split to coding units corresponding to a lower depth.Hereinafter, the coding unit that is no longer split and becomes a basicunit for prediction encoding will now be referred to as a ‘predictionunit’. A partition obtained by splitting the prediction unit may includea prediction unit or a data unit obtained by splitting at least one of aheight and a width of the prediction unit.

For example, when a coding unit of 2N×2N (where N is a positive integer)is no longer split and becomes a prediction unit of 2N×2N, a size of apartition may be 2N×2N, 2N×N, N×2N, or N×N. Examples of a partition typeinclude symmetric partitions that are obtained by symmetricallysplitting a height or width of the prediction unit, partitions obtainedby asymmetrically splitting the height or width of the prediction unit,such as 1:n or n:1, partitions that are obtained by geometricallysplitting the prediction unit, and partitions having arbitrary shapes.

A prediction mode of the prediction unit may be at least one of an intramode, a inter mode, and a skip mode. For example, the intra mode or theinter mode may be performed on the partition of 2N×2N, 2N×N, N×2N, orN×N. Also, the skip mode may be performed only on the partition of2N×2N. The encoding is independently performed on one prediction unit ina coding unit, thereby selecting a prediction mode having a leastencoding error.

The video encoding apparatus 100 may also perform the transformation onthe image data in a coding unit based not only on the coding unit forencoding the image data, but also based on a data unit that is differentfrom the coding unit.

In order to perform the transformation in the coding unit, thetransformation may be performed based on a transformation unit having asize smaller than or equal to the coding unit. For example, thetransformation unit for the transformation may include a data unit foran intra mode and a data unit for an inter mode.

Similarly to the coding unit, the transformation unit in the coding unitmay be recursively split into smaller sized regions, so that thetransformation unit may be determined independently in units of regions.Thus, residual data in the coding unit may be divided according to thetransformation units having the tree structure according totransformation depths.

A transformation depth indicating the number of times splitting isperformed to reach the transformation unit by splitting the height andwidth of the coding unit may also be set in the transformation unit. Forexample, in a current coding unit of 2N×2N, a transformation depth maybe 0 when the size of a transformation unit is also 2N×2N, may be 1 whenthe size of the transformation unit is N×N, and may be 2 when the sizeof the transformation unit is N/2×N/2. In other words, transformationunits having a tree structure may be set according to transformationdepths.

Encoding information according to a coded depth requires not onlyinformation about the coded depth, but also information about predictionencoding and transformation. Accordingly, the encoder 120 not onlydetermines a coded depth having a least encoding error, but alsodetermines a partition type in a prediction unit, a prediction modeaccording to prediction units, and a size of a transformation unit fortransformation. For inter prediction, the encoding information accordingto a coded depth may include information related to interpolationfiltering for interpolating sub-pel units.

Also, the encoder 120 may perform transformation by using transformationunits having a tree structure to encode coding units, based on a maximumsplit level of the transformation units, which is previously andrestrictively set in each maximum coding unit or a current coding unit.

In each of deeper coding units according to depths, a basictransformation unit having a size smaller than or equal to a coding unitmay be hierarchically split into transformation units of lowertransformation depths. Transformation units having a tree structure mayinclude a basic transformation unit having a maximum size that iscurrently allowed, and lower-level transformation units relative to amaximum split level that is allowed for coding units.

After performing transformation in each level according to atransformation depth in a current coding unit, the encoder 120 maydetermine transformation units having a tree structure, which areindependent from transformation units of adjacent regions and form ahierarchical structure between transformation units in the same regionaccording to transformation depths.

In other words, transformation units having a tree structure may bedetermined by performing transformation on each coding unit by usingvarious-sized transformation units and then comparing results oftransformation. While a coding unit is being determined, atransformation unit for transforming the coding unit may be determined.Whenever coding units according to each of one or more depths areencoded, transformation units according to each of one or moretransformation depths may be used to perform transformation.

A transformation unit having a least encoding error has to be determinedfor each coding unit. In order to determine a transformation depthhaving a minimum encoding error in a transformation unit, encodingerrors may be measured and compared in all deeper transformation unitsaccording to depths. A transformation unit may be determined as a dataunit for minimizing a transformation error of a coding unit.

Accordingly, since a combination of a deeper coding unit and a deepertransformation unit according to depths, which has a least encodingerror, is individually determined in each region of a maximum codingunit, coding units having a tree structure and transformation unitshaving a tree structure may be determined.

Methods of determining coding units having a tree structure, partitions,and transformation units having a tree structure in a maximum codingunit, according to exemplary embodiments, will be described in detaillater with reference to FIGS. 15 through 25.

The encoder 120 may measure an encoding error of deeper coding unitsaccording to depths by using rate-distortion optimization based onLagrangian multipliers.

The video encoding apparatus 100 may output the image data of themaximum coding unit, which is encoded based on the at least one codeddepth determined by the encoder 120, and information about a coding modeaccording to the coded depth, which is encoded by the output unit 130,in the form of a bitstream.

The information about the coding mode of deeper coding units accordingto depths, which is determined as a picture is encoded based on codingunits, prediction units, and transformation units having a treestructure, may be included in a header, a sequence parameter set (SPS),or a picture parameter set (PPS) of a bitstream.

The encoded image data may be obtained by encoding residual data of animage.

The information about the coding mode according to the coded depth mayinclude information about the coded depth, about the partition type inthe prediction unit, the prediction mode, and the size of thetransformation unit.

The information about the coded depth may be defined by using splitinformation according to depths, which represents whether encoding isperformed on coding units of a lower depth instead of a current depth.If the current depth of the current coding unit is the coded depth,image data in the current coding unit is encoded and output, and thusthe split information may be defined not to split the current codingunit to a lower depth. Alternatively, if the current depth of thecurrent coding unit is not the coded depth, the encoding is performed onthe coding unit of the lower depth, and thus the split information maybe defined to split the current coding unit to obtain the coding unitsof the lower depth.

If the current depth is not the coded depth, encoding is performed onthe coding unit that is split into the coding unit of the lower depth.Since at least one coding unit of the lower depth exists in one codingunit of the current depth, the encoding is repeatedly performed on eachcoding unit of the lower depth, and thus the encoding may be recursivelyperformed for the coding units having the same depth.

Since the coding units having a tree structure are determined for onemaximum coding unit, and information about at least one coding mode isdetermined for a coding unit of a coded depth, information about atleast one coding mode may be determined for one maximum coding unit.Also, a coded depth of the image data of the maximum coding unit may bedifferent according to locations since the image data is hierarchicallysplit according to depths, and thus information about the coded depthand the coding mode may be set for the image data.

Accordingly, the output unit 130 may assign encoding information about acorresponding coded depth and a coding mode to at least one of thecoding unit, the prediction unit, and a minimum unit included in themaximum coding unit.

The minimum unit according to an exemplary embodiment is a rectangulardata unit obtained by splitting the minimum coding unit constituting thelowermost depth by 4. Alternatively, the minimum unit may be a maximumrectangular data unit that may be included in all of the coding units,prediction units, partition units, and transformation units included inthe maximum coding unit.

For example, the encoding information output through the output unit 130may be classified into encoding information according to coding units,and encoding information according to prediction units. The encodinginformation according to the coding units may include the informationabout the prediction mode and about the size of the partitions. Theencoding information according to the prediction units may includeinformation about an estimated direction of an inter mode, about areference image index of the inter mode, about a motion vector, about achroma component of an intra mode, and about an interpolation method ofthe intra mode.

Information about a maximum size of the coding unit defined according topictures, slices, or GOPs, and information about a maximum depth may beinserted into a header, an SPS, or a PPS of a bitstream.

In the video encoding apparatus 100, the deeper coding unit may be acoding unit obtained by dividing a height or width of a coding unit ofan upper depth, which is one layer above, by two. In other words, whenthe size of the coding unit of the current depth is 2N×2N, the size ofthe coding unit of the lower depth is N×N. Also, the coding unit of thecurrent depth having the size of 2N×2N may include maximum 4 of thecoding unit of the lower depth.

Accordingly, the video encoding apparatus 100 may form the coding unitshaving the tree structure by determining coding units having an optimumshape and an optimum size for each maximum coding unit, based on thesize of the maximum coding unit and the maximum depth determinedconsidering characteristics of the current picture. Also, since encodingmay be performed on each maximum coding unit by using any one of variousprediction modes and transformations, an optimum coding mode may bedetermined considering characteristics of the coding unit of variousimage sizes.

Thus, if an image having high resolution or large data amount is encodedin a conventional macroblock, a number of macroblocks per pictureexcessively increases. Accordingly, a number of pieces of compressedinformation generated for each macroblock increases, and thus it isdifficult to transmit the compressed information and data compressionefficiency decreases. However, by using the video encoding apparatus100, image compression efficiency may be increased since a coding unitis adjusted while considering characteristics of an image whileincreasing a maximum size of a coding unit while considering a size ofthe image.

The output unit 130 may encode and output encoding informationindicating an encoding method used to encode a video based on codingunits having a tree structure and transformation units having a treestructure. The encoding information may include information aboutvarious coding modes of coding units corresponding to a coded depth, andinformation about the coded depth.

Definitions of various terms, such as a coding unit, a depth, aprediction unit, a transformation unit, and information about variouscoding modes, for various operations of the video decoding apparatus 200are identical to those described with reference to the video encodingapparatus 100.

The receiver 210 receives a bitstream of an encoded video. The receiverand extractor 220 parses the received bitstream. The receiver andextractor 220 extracts encoded picture data for each coding unit fromthe parsed bitstream, wherein the coding units have a tree structureaccording to each maximum coding unit, and outputs the extracted picturedata to the decoder 230. The receiver and extractor 220 may extractinformation about a maximum size of a coding unit of a current picture,from a header, an SPS, or a PPS about the current picture.

Also, the receiver and extractor 220 may extract encoding informationabout the coding units having a tree structure according to each maximumcoding unit, from the parsed bitstream. Information about a coded depthand a coding mode is extracted from the encoding information. Theextracted information about the coded depth and the coding mode isoutput to the decoder 230. In other words, the image data in a bitstreammay be split into the maximum coding unit so that the decoder 230 maydecode the image data for each maximum coding unit.

The information about the coded depth and the coding mode according tothe maximum coding unit may be set for information about at least onecoding unit corresponding to the coded depth, and information about acoding mode may include information about a partition type of acorresponding coding unit corresponding to the coded depth, about aprediction mode, and a size of a transformation unit. For interprediction, information related to interpolation filtering forinterpolating sub-pel units may be extracted from the encodinginformation according to a coded depth. Also, splitting informationaccording to depths may be extracted as the information about the codeddepth.

The information about the coded depth and the coding mode according toeach maximum coding unit extracted by the receiver and extractor 220 isinformation about a coded depth and a coding mode determined to generatea minimum encoding error when an encoder, such as the video encodingapparatus 100, repeatedly performs encoding for each deeper coding unitaccording to depths according to each maximum coding unit. Accordingly,the video decoding apparatus 200 may restore an image by decoding theimage data according to a coded depth and a coding mode that generatesthe minimum encoding error.

Since encoding information about the coded depth and the coding mode maybe assigned to a predetermined data unit from among a correspondingcoding unit, a prediction unit, and a minimum unit, the receiver andextractor 220 may extract the information about the coded depth and thecoding mode according to the predetermined data units. The predetermineddata units to which the same information about the coded depth and thecoding mode is assigned may be inferred to be the data units included inthe same maximum coding unit.

The decoder 230 may determine at least one coded depth of a currentmaximum coding unit by using split information according to depths. Ifthe split information represents that image data is no longer split inthe current depth, the current depth is a coded depth. Accordingly, thedecoder 230 may decode encoded picture data of at least one coding unitcorresponding to the each coded depth in the current maximum coding unitby using the information about the partition type of the predictionunit, the prediction mode, and the size of the transformation unit foreach coding unit corresponding to the coded depth, and output the imagedata of the current maximum coding unit.

In other words, data units containing the encoding information includingthe same split information may be gathered by observing the encodinginformation set assigned for the predetermined data unit from among thecoding unit, the prediction unit, and the minimum unit, and the gathereddata units may be considered to be one data unit to be decoded by thedecoder 230 in the same coding mode.

The decoder 230 may restore the current picture by decoding the encodedpicture data in each maximum coding unit based on the information aboutthe coded depth and the coding mode according to the maximum codingunits. The partition type, the prediction mode, and the transformationunit may be read as the coding mode for each coding unit from among thecoding units having the tree structure included in each maximum codingunit. A decoding process may include a prediction including intraprediction and motion compensation, and an inverse transformation.

The decoder 230 may perform intra prediction or motion compensationaccording to a partition and a prediction mode of each coding unit,based on the information about the partition type and the predictionmode of the prediction unit of the coding units having a tree structure.

Also, the decoder 230 may read the structure of transformation unitshaving a tree structure and may perform inverse transformation on eachcoding unit based on the transformation units.

The video decoding apparatus 200 may obtain information about at leastone coding unit that generates the minimum encoding error when encodingis recursively performed for each maximum coding unit, and may use theinformation to decode the current picture. In other words, the codingunits having the tree structure determined to be the optimum codingunits in each maximum coding unit may be decoded. Also, the maximum sizeof coding unit is determined in consideration of resolution and anamount of image data.

Accordingly, even if image data has high resolution and a large amountof data, the image data may be efficiently decoded and restored by usinga size of a coding unit and a coding mode, which are adaptivelydetermined according to characteristics of the image data, by usinginformation about an optimum coding mode received from an encoder.

FIG. 15 is a diagram for describing a concept of coding units accordingto an exemplary embodiment.

A size of a coding unit may be expressed in width×height, and may be64×64, 32×32, 16×16, and 8×8. A coding unit of 64×64 may be split intopartitions of 64×64, 64×32, 32×64, or 32×32, a coding unit of 32×32 maybe split into partitions of 32×32, 32×16, 16×32, or 16×16, a coding unitof 16×16 may be split into partitions of 16×16, 16×8, 8×16, or 8×8, anda coding unit of 8×8 may be split into partitions of 8×8, 8×4, 4×8, or4×4.

In video data 310, a resolution is 1920×1080, a maximum size of a codingunit is 64, and a maximum depth is 2. In video data 320, a resolution is1920×1080, a maximum size of a coding unit is 64, and a maximum depth is3. In video data 330, a resolution is 352×288, a maximum size of acoding unit is 16, and a maximum depth is 1. The maximum depth shown inFIG. 15 denotes a total number of splits from a maximum coding unit to aminimum decoding unit.

If a resolution is high or a data amount is large, a maximum size of acoding unit may be large so as to not only increase encoding efficiencybut also to accurately reflect characteristics of an image. Accordingly,the maximum size of the coding unit of the video data 310 and 320 havingthe higher resolution than the video data 330 may be 64.

Since the maximum depth of the video data 310 is 2, coding units 315 ofthe video data 310 may include a maximum coding unit having a long axissize of 64, and coding units having long axis sizes of 32 and 16 sincedepths are deepened to two layers by splitting the maximum coding unittwice. Meanwhile, since the maximum depth of the video data 330 is 1,coding units 335 of the video data 330 may include a maximum coding unithaving a long axis size of 16, and coding units having a long axis sizeof 8 since depths are deepened to one layer by splitting the maximumcoding unit once.

Since the maximum depth of the video data 320 is 3, coding units 325 ofthe video data 320 may include a maximum coding unit having a long axissize of 64, and coding units having long axis sizes of 32, 16, and 8since the depths are deepened to 3 layers by splitting the maximumcoding unit three times. As a depth deepens, detailed information may beprecisely expressed.

FIG. 16 is a block diagram of an image encoder 400 based on codingunits, according to an exemplary embodiment.

The image encoder 400 performs operations of the encoder 120 of thevideo encoding apparatus 100 to encode image data. In other words, anintra predictor 410 performs intra prediction on coding units in anintra mode, from among a current frame 405, and a motion estimator 420and a motion compensator 425 performs inter estimation and motioncompensation on coding units in an inter mode from among the currentframe 405 by using the current frame 405, and a reference frame 495.

In order to precisely perform motion estimation by using referencepixels in sub-pel units, the motion estimator 420 and the motioncompensator 425 may generate pixels in sub-pel units by interpolatingpixels in integer-pel units. An interpolation filter for generatingpixels in sub-pel units may be the interpolation filter described abovein relation to FIGS. 1 and 13A.

Data output from the intra predictor 410, the motion estimator 420, andthe motion compensator 425 is output as a quantized transformationcoefficient through a transformer 430 and a quantizer 440. The quantizedtransformation coefficient is restored as data in a spatial domainthrough an inverse quantizer 460 and an inverse transformer 470, and therestored data in the spatial domain is output as the reference frame 495after being post-processed through a deblocking unit 480 and a loopfiltering unit 490. The quantized transformation coefficient may beoutput as a bitstream 455 through an entropy encoder 450.

In order for the image encoder 400 to be applied in the video encodingapparatus 100, all elements of the image encoder 400, i.e., the intrapredictor 410, the motion estimator 420, the motion compensator 425, thetransformer 430, the quantizer 440, the entropy encoder 450, the inversequantizer 460, the inverse transformer 470, the deblocking unit 480, andthe loop filtering unit 490, have to perform operations based on eachcoding unit from among coding units having a tree structure whileconsidering the maximum depth of each maximum coding unit.

Specifically, the intra predictor 410, the motion estimator 420, and themotion compensator 425 have to determine partitions and a predictionmode of each coding unit from among the coding units having a treestructure while considering the maximum size and the maximum depth of acurrent maximum coding unit, and the transformer 430 has to determinethe size of the transformation unit in each coding unit from among thecoding units having a tree structure.

FIG. 17 is a block diagram of an image decoder 500 based on codingunits, according to an exemplary embodiment.

A parser 510 parses encoded image data to be decoded and informationabout encoding required for decoding from a bitstream 505. The encodedimage data is output as inversely quantized data through an entropydecoder 520 and an inverse quantizer 530, and the inversely quantizeddata is restored to image data in a spatial domain through an inversetransformer 540.

An intra predictor 550 performs intra prediction on coding units in anintra mode with respect to the image data in the spatial domain, and amotion compensator 560 performs motion compensation on coding units inan inter mode by using a reference frame 585.

In order to precisely perform motion estimation by using referencepixels in sub-pel units, the motion compensator 560 may generate pixelsin sub-pel units by interpolating pixels in integer-pel units. Aninterpolation filter for generating pixels in sub-pel units may be theinterpolation filter described above in relation to FIGS. 2 and 13B.

The image data in the spatial domain, which passed through the intrapredictor 550 and the motion compensator 560, may be output as arestored frame 595 after being post-processed through a deblocking unit(also referred to herein as a “deblocker”) 570 and a loop filtering unit(also referred to herein as a “loop filter”) 580. Also, the image datathat is post-processed through the deblocking unit 570 and the loopfiltering unit 580 may be output as the reference frame 585.

In order to decode the image data in the decoder 230 of the videodecoding apparatus 200, the image decoder 500 may perform operationsthat are performed after the parser 510.

In order for the image decoder 500 to be applied in the video decodingapparatus 200, all elements of the image decoder 500, i.e., the parser510, the entropy decoder 520, the inverse quantizer 530, the inversetransformer 540, the intra predictor 550, the motion compensator 560,the deblocking unit 570, and the loop filtering unit 580, have toperform operations based on coding units having a tree structure foreach maximum coding unit.

Specifically, the intra predictor 550 and the motion compensator 560have to determine partitions and a prediction mode for each of thecoding units having a tree structure, and the inverse transformer 540has to determine a size of a transformation unit for each coding unit.

FIG. 18 is a diagram illustrating deeper coding units according todepths, and partitions, according to an exemplary embodiment.

The video encoding apparatus 100 and the video decoding apparatus 200use hierarchical coding units so as to consider characteristics of animage. A maximum height, a maximum width, and a maximum depth of codingunits may be adaptively determined according to the characteristics ofthe image, or may be differently set by a user. Sizes of deeper codingunits according to depths may be determined according to thepredetermined maximum size of the coding unit.

In a hierarchical structure 600 of coding units, according to anexemplary embodiment, the maximum height and the maximum width of thecoding units are each 64, and the maximum depth is 4. In this case, themaximum depth denotes the total number of times splitting is performedfrom a maximum coding unit to a minimum coding unit. Since a depthdeepens along a vertical axis of the hierarchical structure 600, aheight and a width of the deeper coding unit are each split. Also, aprediction unit and partitions, which are bases for prediction encodingof each deeper coding unit, are shown along a horizontal axis of thehierarchical structure 600.

In other words, a coding unit 610 is a maximum coding unit in thehierarchical structure 600, wherein a depth is 0 and a size, i.e., aheight by width, is 64×64. The depth deepens along the vertical axis,and a coding unit 620 having a size of 32×32 and a depth of 1, a codingunit 630 having a size of 16×16 and a depth of 2, and a coding unit 640having a size of 8×8 and a depth of 3. The coding unit 640 having thesize of 8×8 and the depth of 3 is a minimum coding unit.

The prediction unit and the partitions of a coding unit are arrangedalong the horizontal axis according to each depth. In other words, ifthe coding unit 610 having the size of 64×64 and the depth of 0 is aprediction unit, the prediction unit may be split into partitionsincluded in the coding unit 610, i.e. a partition 610 having a size of64×64, partitions 612 having the size of 64×32, partitions 614 havingthe size of 32×64, or partitions 616 having the size of 32×32.

Similarly, a prediction unit of the coding unit 620 having the size of32×32 and the depth of 1 may be split into partitions included in thecoding unit 620, i.e. a partition 620 having a size of 32×32, partitions622 having a size of 32×16, partitions 624 having a size of 16×32, orpartitions 626 having a size of 16×16.

Similarly, a prediction unit of the coding unit 630 having the size of16×16 and the depth of 2 may be split into partitions included in thecoding unit 630, i.e. a partition having a size of 16×16, partitions 632having a size of 16×8, partitions 634 having a size of 8×16, orpartitions 636 having a size of 8×8.

Similarly, a prediction unit of the coding unit 640 having the size of8×8 and the depth of 3 may be split into partitions included in thecoding unit 640, i.e. a partition having a size of 8×8, partitions 642having a size of 8×4, partitions 644 having a size of 4×8, or partitions646 having a size of 4×4.

In order to determine the at least one coded depth of the coding unitsconstituting the maximum coding unit 610, the encoder 120 of the videoencoding apparatus 100 performs encoding for coding units correspondingto each depth included in the maximum coding unit 610.

A number of deeper coding units according to depths including data inthe same range and the same size increases as the depth deepens. Forexample, four coding units corresponding to a depth of 2 are required tocover data that is included in one coding unit corresponding to a depthof 1. Accordingly, in order to compare encoding results of the same dataaccording to depths, the coding unit corresponding to the depth of 1 andfour coding units corresponding to the depth of 2 are each encoded.

In order to perform encoding for a current depth from among the depths,a least encoding error may be selected for the current depth byperforming encoding for each prediction unit in the coding unitscorresponding to the current depth, along the horizontal axis of thehierarchical structure 600. Alternatively, the minimum encoding errormay be searched for by comparing the least encoding errors according todepths, by performing encoding for each depth as the depth deepens alongthe vertical axis of the hierarchical structure 600. A depth and apartition having the minimum encoding error in the coding unit 610 maybe selected as the coded depth and a partition type of the coding unit610.

FIG. 19 is a diagram for describing a relationship between a coding unit710 and transformation units 720, according to an exemplary embodiment.

The video encoding apparatus 100 or the video decoding apparatus 200encodes or decodes an image according to coding units having sizessmaller than or equal to a maximum coding unit for each maximum codingunit. Sizes of transformation units for transformation during encodingmay be selected based on data units that are not larger than acorresponding coding unit.

For example, in the video encoding apparatus 100 or the video decodingapparatus 200, if a size of the coding unit 710 is 64×64, transformationmay be performed by using the transformation units 720 having a size of32×32.

Also, data of the coding unit 710 having the size of 64×64 may beencoded by performing the transformation on each of the transformationunits having the size of 32×32, 16×16, 8×8, and 4×4, which are smallerthan 64×64, and then a transformation unit having the least coding errormay be selected.

FIG. 20 is a diagram for describing encoding information of coding unitscorresponding to a coded depth, according to an exemplary embodiment.

The output unit 130 of the video encoding apparatus 100 may encode andtransmit information 800 about a partition type, information 810 about aprediction mode, and information 820 about a size of a transformationunit for each coding unit corresponding to a coded depth, as informationabout a coding mode.

The information 800 represents information about a shape of a partitionobtained by splitting a prediction unit of a current coding unit,wherein the partition is a data unit for prediction encoding the currentcoding unit. For example, a current coding unit CU_(—)0 having a size of2N×2N may be split into any one of a partition 802 having a size of2N×2N, a partition 804 having a size of 2N×N, a partition 806 having asize of N×2N, and a partition 808 having a size of N×N. Here, theinformation 800 about a partition type is set to indicate one of thepartition 804 having a size of 2N×N, the partition 806 having a size ofN×2N, and the partition 808 having a size of N×N

The information 810 represents a prediction mode of each partition. Forexample, the information 810 may indicate a mode of prediction encodingperformed on a partition represented by the information 800, i.e., anintra mode 812, an inter mode 814, or a skip mode 816.

The information 820 represents a transformation unit to be based on whentransformation is performed on a current coding unit. For example, thetransformation unit may be a first intra transformation unit 822, asecond intra transformation unit 824, a first inter transformation unit826, or a second inter transformation unit 828.

The receiver and extractor 220 of the video decoding apparatus 200 mayextract and use the information 800, 810, and 820 for decoding,according to each deeper coding unit

FIG. 21 is a diagram of deeper coding units according to depths,according to an exemplary embodiment.

Split information may be used to indicate a change of a depth. The spiltinformation represents whether a coding unit of a current depth is splitinto coding units of a lower depth.

A prediction unit 910 for prediction encoding a coding unit 900 having adepth of 0 and a size of 2N_(—)0×2N_(—)0 may include partitions of apartition type 912 having a size of 2N_(—)0×2N_(—)0, a partition type914 having a size of 2N_(—)0×N_(—)0, a partition type 916 having a sizeof N_(—)0×2N_(—)0, and a partition type 918 having a size ofN_(—)0×N_(—)0. FIG. 21 only illustrates the partition types 912 through918 which are obtained by symmetrically splitting the prediction unit910, but a partition type is not limited thereto, and the partitions ofthe prediction unit 910 may include asymmetric partitions, partitionshaving a predetermined shape, and partitions having a geometrical shape.

Prediction encoding is repeatedly performed on one partition having asize of 2N_(—)0×2N_(—)0, two partitions having a size of 2N_(—)0×N_(—)0,two partitions having a size of N_(—)0×2N_(—)0, and four partitionshaving a size of N_(—)0×N_(—)0, according to each partition type. Theprediction encoding in an intra mode and an inter mode may be performedon the partitions having the sizes of 2N_(—)0×2N_(—)0, N_(—)0×2N_(—)0,2N_(—)0×N_(—)0, and N_(—)0×N_(—)0. The prediction encoding in a skipmode is performed only on the partition having the size of2N_(—)0×2N_(—)0.

Errors of encoding including the prediction encoding in the partitiontypes 912 through 918 are compared, and the least encoding error isdetermined among the partition types. If an encoding error is smallestin one of the partition types 912 through 916, the prediction unit 910may not be split into a lower depth.

If the encoding error is the smallest in the partition type 918, a depthis changed from 0 to 1 to split the partition type 918 in operation 920,and encoding is repeatedly performed on coding units 930 having a depthof 2 and a size of N_(—)0×N_(—)0 to search for a minimum encoding error.

A prediction unit 940 for prediction encoding the coding unit 930 havinga depth of 1 and a size of 2N_(—)1×2N_(—)1 (=N_(—)0×N_(—)0) may includepartitions of a partition type 942 having a size of 2N_(—)1×2N_(—)1, apartition type 944 having a size of 2N_(—)1×N_(—)1, a partition type 946having a size of N_(—)1×2N_(—)1, and a partition type 948 having a sizeof N_(—)1×N_(—)1.

If an encoding error is the smallest in the partition type 948, a depthis changed from 1 to 2 to split the partition type 948 in operation 950,and encoding is repeatedly performed on coding units 960, which have adepth of 2 and a size of N_(—)2×N_(—)2 to search for a minimum encodingerror.

When a maximum depth is d, deeper coding units according to depths maybe assigned up to when a depth becomes d−1, and split information may beencoded as up to when a depth is one of 0 to d−2. In other words, whenencoding is performed up to when the depth is d−1 after a coding unitcorresponding to a depth of d−2 is split in operation 970, a predictionunit 990 for prediction encoding a coding unit 980 having a depth of d−1and a size of 2N_(d−1)×2N_(d−1) may include partitions of a partitiontype 992 having a size of 2N_(d−1)×2N_(d−1), a partition type 994 havinga size of 2N_(d−1)×N_(d−1), a partition type 996 having a size ofN_(d−1)×2N_(d−1), and a partition type 998 having a size ofN_(d−1)×N_(d−1).

Prediction encoding may be repeatedly performed on one partition havinga size of 2N_(d−1)×2N_(d−1), two partitions having a size of2N_(d−1)×N_(d−1), two partitions having a size of N_(d−1)×2N_(d−1), fourpartitions having a size of N_(d−1)×N_(d−1) from among the partitiontypes 992 through 998 so as to search for a partition type having aminimum encoding error.

Even when the partition type 998 has the minimum encoding error, since amaximum depth is d, a coding unit CU_(d−1) having a depth of d−1 is nolonger split to a lower depth, and a coded depth for the coding unitsconstituting a current maximum coding unit 900 is determined to be d−1and a partition type of the current maximum coding unit 900 may bedetermined to be N_(d−1)×N_(d−1). Also, since the maximum depth is d anda minimum coding unit 980 having a lowermost depth of d−1 is no longersplit to a lower depth, split information for the minimum coding unit980 is not set.

A data unit 999 may be a ‘minimum unit’ for the current maximum codingunit. A minimum unit according to an exemplary embodiment may be arectangular data unit obtained by splitting a minimum coding unit 980 by4. By performing the encoding repeatedly, the video encoding apparatus100 may select a depth having the least encoding error by comparingencoding errors according to depths of the coding unit 900 to determinea coded depth, and set a corresponding partition type and a predictionmode as a coding mode of the coded depth.

As such, the minimum encoding errors according to depths are compared inall of the depths of 1 through d, and a depth having the least encodingerror may be determined as a coded depth. The coded depth, the partitiontype of the prediction unit, and the prediction mode may be encoded andtransmitted as information about a coding mode. Also, since a codingunit is split from a depth of 0 to a coded depth, only split informationof the coded depth is set to 0, and split information of depthsexcluding the coded depth is set to 1.

The receiver and extractor 220 of the video decoding apparatus 200 mayextract and use the information about the coded depth and the predictionunit of the coding unit 900 to decode the partition 912. The videodecoding apparatus 200 may determine a depth, in which split informationis 0, as a coded depth by using split information according to depths,and use information about a coding mode of the corresponding depth fordecoding.

FIGS. 22, 23, and 24 are diagrams for describing a relationship betweencoding units 1010, prediction units 1060, and transformation units 1070,according to an exemplary embodiment.

The coding units 1010 are coding units having a tree structure,corresponding to coded depths determined by the video encoding apparatus100, in a maximum coding unit. The prediction units 1060 are partitionsof prediction units of each of the coding units 1010, and thetransformation units 1070 are transformation units of each of the codingunits 1010.

When a depth of a maximum coding unit is 0 in the coding units 1010,depths of coding units 1012 and 1054 are 1, depths of coding units 1014,1016, 1018, 1028, 1050, and 1052 are 2, depths of coding units 1020,1022, 1024, 1026, 1030, 1032, and 1048 are 3, and depths of coding units1040, 1042, 1044, and 1046 are 4.

In the prediction units 1060, some coding units 1014, 1016, 1022, 1032,1048, 1050, 1052, and 1054 are obtained by splitting the coding units inthe coding units 1010. In other words, partition types in the codingunits 1014, 1022, 1050, and 1054 have a size of 2N×N, partition types inthe coding units 1016, 1048, and 1052 have a size of N×2N, and apartition type of the coding unit 1032 has a size of N×N. Predictionunits and partitions of the coding units 1010 are smaller than or equalto each coding unit.

Transformation or inverse transformation is performed on image data ofthe coding unit 1052 in the transformation units 1070 in a data unitthat is smaller than the coding unit 1052. Also, the coding units 1014,1016, 1022, 1032, 1048, 1050, and 1052 in the transformation units 1070are different from those in the prediction units 1060 in terms of sizesand shapes. In other words, the video encoding and decoding apparatuses100 and 200 may perform intra prediction, motion estimation, motioncompensation, transformation, and inverse transformation individually ona data unit in the same coding unit.

Accordingly, encoding is recursively performed on each of coding unitshaving a hierarchical structure in each region of a maximum coding unitto determine an optimum coding unit, and thus coding units having arecursive tree structure may be obtained. Encoding information mayinclude split information about a coding unit, information about apartition type, information about a prediction mode, and informationabout a size of a transformation unit. Table 1 shows the encodinginformation that may be set by the video encoding and decodingapparatuses 100 and 200.

TABLE 1 Split Information 0 (Encoding on Coding Unit having Size of 2N ×2N and Current Depth of d) Size of Transformation Unit Split SplitPartition Type Information 0 Information 1 Symmetric Asymmetric of ofPrediction Partition Partition Transformation Transformation Split ModeType Type Unit Unit Information 1 Intra 2N × 2N 2N × nU 2N × 2N N × NRepeatedly Inter 2N × N  2N × nD (Symmetric Encode Skip  N × 2N nL × 2NPartition Coding Units (Only N × N nR × 2N Type) having Lower 2N × 2N)N/2 × N/2 Depth of d + 1 (Asymmetric Partition Type)

The output unit 130 of the video encoding apparatus 100 may output theencoding information about the coding units having a tree structure, andthe receiver and extractor 220 of the video decoding apparatus 200 mayextract the encoding information about the coding units having a treestructure from a received bitstream.

Split information represents whether a current coding unit is split intocoding units of a lower depth. If split information of a current depth dis 0, a depth, in which a current coding unit is no longer split into alower depth, is a coded depth, and thus information about a partitiontype, prediction mode, and a size of a transformation unit may bedefined for the coded depth. If the current coding unit is further splitaccording to the split information, encoding is independently performedon four split coding units of a lower depth.

A prediction mode may be one of an intra mode, an inter mode, and a skipmode. The intra mode and the inter mode may be defined in all partitiontypes, and the skip mode is defined only in a partition type having asize of 2N×2N.

The information about the partition type may indicate symmetricpartition types having sizes of 2N×2N, 2N×N, N×2N, and N×N, which areobtained by symmetrically splitting a height or a width of a predictionunit, and asymmetric partition types having sizes of 2N×nU, 2N×nD,nL×2N, and nR×2N, which are obtained by asymmetrically splitting theheight or width of the prediction unit. The asymmetric partition typeshaving the sizes of 2N×nU and 2N×nD may be respectively obtained bysplitting the height of the prediction unit in 1:3 and 3:1, and theasymmetric partition types having the sizes of nL×2N and nR×2N may berespectively obtained by splitting the width of the prediction unit in1:3 and 3:1

The size of the transformation unit may be set to be two types in theintra mode and two types in the inter mode. In other words, if splitinformation of the transformation unit is 0, the size of thetransformation unit may be 2N×2N, which is the size of the currentcoding unit. If split information of the transformation unit is 1, thetransformation units may be obtained by splitting the current codingunit. Also, if a partition type of the current coding unit having thesize of 2N×2N is a symmetric partition type, a size of a transformationunit may be N×N, and if the partition type of the current coding unit isan asymmetric partition type, the size of the transformation unit may beN/2×N/2.

The encoding information about coding units having a tree structure mayinclude at least one of a coding unit corresponding to a coded depth, aprediction unit, and a minimum unit. The coding unit corresponding tothe coded depth may include at least one of a prediction unit and aminimum unit containing the same encoding information.

Accordingly, it is determined whether adjacent data units are includedin the same coding unit corresponding to the coded depth by comparingencoding information of the adjacent data units. Also, a correspondingcoding unit corresponding to a coded depth is determined by usingencoding information of a data unit, and thus a distribution of codeddepths in a maximum coding unit may be determined.

Accordingly, if a current coding unit is predicted based on encodinginformation of adjacent data units, encoding information of data unitsin deeper coding units adjacent to the current coding unit may bedirectly referred to and used.

Alternatively, if a current coding unit is predicted based on encodinginformation of adjacent data units, data units adjacent to the currentcoding unit are searched using encoded information of the data units,and the searched adjacent coding units may be referred to for predictingthe current coding unit.

FIG. 25 is a diagram for describing a relationship between a codingunit, a prediction unit or a partition, and a transformation unit,according to coding mode information of Table 1.

A maximum coding unit 1300 includes coding units 1302, 1304, 1306, 1312,1314, 1316, and 1318 of coded depths. Here, since the coding unit 1318is a coding unit of a coded depth, split information may be set to 0.Information about a partition type of the coding unit 1318 having a sizeof 2N×2N may be set to be one of a partition type 1322 having a size of2N×2N, a partition type 1324 having a size of 2N×N, a partition type1326 having a size of N×2N, a partition type 1328 having a size of N×N,a partition type 1332 having a size of 2N×nU, a partition type 1334having a size of 2N×nD, a partition type 1336 having a size of nL×2N,and a partition type 1338 having a size of nR×2N.

Split information (TU size flag) of a transformation unit is a sort of atransformation index, and the size of a transformation unitcorresponding to the transformation index may vary according to aprediction unit type or a partition type of a coding unit.

For example, when the partition type is set to be symmetric, i.e. thepartition type 1322, 1324, 1326, or 1328, a transformation unit 1342having a size of 2N×2N is set if a TU size flag is 0, and atransformation unit 1344 having a size of N×N is set if a TU size flagis 1.

When the partition type is set to be asymmetric, i.e., the partitiontype 1332, 1334, 1336, or 1338, a transformation unit 1352 having a sizeof 2N×2N is set if a TU size flag is 0, and a transformation unit 1354having a size of N/2×N/2 is set if a TU size flag is 1.

Referring to FIG. 21, the TU size flag is a flag having a value or 0 or1, but the TU size flag is not limited to 1 bit, and a transformationunit may be hierarchically split having a tree structure while the TUsize flag increases from 0. The TU size flag may be used as an exampleof a transformation index.

In this case, the size of a transformation unit that has been actuallyused may be expressed by using a TU size flag of a transformation unit,according to an embodiment of the present invention, together with amaximum size and minimum size of the transformation unit. According toan exemplary embodiment, the video encoding apparatus 100 is capable ofencoding maximum transformation unit size information, minimumtransformation unit size information, and a maximum TU size flag. Theencoding result of the maximum transformation unit size information, theminimum transformation unit size information, and the maximum TU sizeflag may be inserted into an SPS. According to an embodiment of thepresent invention, the video decoding apparatus 200 may decode video byusing the maximum transformation unit size information, the minimumtransformation unit size information, and the maximum TU size flag.

For example, (a) if the size of a current coding unit is 64×64 and amaximum transformation unit size is 32×32, then (a−1) the size of atransformation unit may be 32×32 when a TU size flag is 0, (a−2) may be16×16 when the TU size flag is 1, and (a−3) may be 8×8 when the TU sizeflag is 2.

As another example, (b) if the size of the current coding unit is 32×32and a minimum transformation unit size is 32×32, then (b−1) the size ofthe transformation unit may be 32×32 when the TU size flag is 0. Here,the TU size flag cannot be set to a value other than 0, since the sizeof the transformation unit cannot be less than 32×32.

As another example, (c) if the size of the current coding unit is 64×64and a maximum TU size flag is 1, then the TU size flag may be 0 or 1.Here, the TU size flag cannot be set to a value other than 0 or 1.

Thus, if it is defined that the maximum TU size flag is‘MaxTransformSizeIndex’, a minimum transformation unit size is‘MinTransformSize’, and a root transformation unit size is ‘RootTuSize’when the TU size flag is 0, then a current minimum transformation unitsize ‘CurrMinTuSize’ that can be determined in a current coding unit,may be defined by Equation (1):

CurrMinTuSize=max(MinTransformSize,RootTuSize/(2″MaxTransformSizeIndex))  (1)

Compared to the current minimum transformation unit size ‘CurrMinTuSize’that can be determined in the current coding unit, the roottransformation unit size ‘RootTuSize’ may denote a maximumtransformation unit size that may be selected in the system. In Equation(1), ‘RootTuSize/(2̂MaxTransformSizeIndex)’ denotes a transformation unitsize when the root transformation unit size ‘RootTuSize’ is split anumber of times corresponding to the maximum TU size flag, and‘MinTransformSize’ denotes a minimum transformation size. Thus, asmaller value from among ‘RootTuSize/(2̂MaxTransformSizeIndex)’ and‘MinTransformSize’ may be the current minimum transformation unit size‘CurrMinTuSize’ that may be determined in the current coding unit.

According to an exemplary embodiment, the root transformation unit size‘RootTuSize’ may vary according to the type of a prediction mode.

For example, if a current prediction mode is an inter mode, then‘RootTuSize’ may be determined by using Equation (2) below. In Equation(2), ‘MaxTransformSize’ denotes a maximum transformation unit size, and‘PUSize’ denotes a current prediction unit size.

RootTuSize=min(MaxTransformSize,PUSize)  (2)

That is, if the current prediction mode is the inter mode, the roottransformation unit size ‘RootTuSize’ when the TU size flag is 0 may bea smaller value from among the maximum transformation unit size and thecurrent prediction unit size.

If a prediction mode of a current partition unit is an intra mode,‘RootTuSize’ may be determined by using Equation (3) below. In Equation(3), ‘PartitionSize’ denotes the size of the current partition unit.

RootTuSize=min(MaxTransformSize,PartitionSize)  (3)

That is, if the current prediction mode is the intra mode, the roottransformation unit size ‘RootTuSize’ may be a smaller value from amongthe maximum transformation unit size and the size of the currentpartition unit.

However, the current maximum transformation unit size that variesaccording to the type of a prediction mode in a partition unit, the roottransformation unit size ‘RootTuSize’, is just an example and thepresent invention is not limited thereto.

FIG. 26 is a flowchart of a video encoding method using an interpolationfilter based on coding units having a tree structure, according to anexemplary embodiment.

In operation 2610, in order to encode a current picture of an inputvideo, the current picture is split into at least one maximum codingunit. Each of at least one split region, which is obtained by splittinga region of each maximum coding unit according to depths, may beencoded. In order to encode each split region according to depths,transformation and quantization are performed on an inter predictionresult based on sub-pel-unit interpolation, and intra prediction.

Here, a split depth for outputting a final encoding result according tothe at least one split region may be determined by comparing results ofencoding split regions according to depths, and coding units included ina current maximum coding unit and having a tree structure may bedetermined. Like the coding units having a tree structure,transformation units having a tree structure may be determined. In otherwords, as an encoding result of a picture, like the determined codingunits having a tree structure, an encoding result of the transformationunits having a tree structure may be output as encoded data of thepicture.

Inter prediction may be performed on each prediction unit or partitionof the coding unit. Motion of a current prediction unit or partition maybe predicted with reference to pixels generated by performingsub-pel-unit interpolation. From among interpolation filters forgenerating a sub-pel-unit pixel value, an interpolation filter isdifferently selected based on a sub-pel-unit interpolation location. Inorder to efficiently perform image interpolation, interpolation filtercoefficients may be selectively determined. The interpolation filter maybe selected as a symmetric or asymmetric interpolation filter accordingto an interpolation location. The interpolation filter may be an odd- oreven-number-tap interpolation filter.

From among interpolation filter coefficients previously stored inmemory, a desired interpolation filter may be selected according to asub-pel-unit interpolation location, a smoothness, the number of filtertaps, a bit depth, a scaling ratio, a basis function of interpolationfiltering based on transformation, a window filter size, and a colorcomponent, and interpolation may be performed to generate thesub-pel-unit pixel value.

In operation 2620, image data obtained as the final encoding resultaccording to the at least one split region of each maximum coding unit,and information about the coded depth and the coding mode are output asa bitstream.

The information about the coding mode may include information about thecoded depth or split information, information about a partition type ofa prediction unit, information about a prediction mode, and informationabout a tree structure of transformation units. The encoding informationmay include information about an interpolation filter used to performsub-pel-unit prediction encoding. The encoded information about thecoding mode may be transmitted to a decoding apparatus together with theencoded image data.

FIG. 27 is a flowchart of a video decoding method using an interpolationfilter based on coding units having a tree structure, according to anexemplary embodiment.

In operation 2710, a bitstream of an encoded video is received andparsed.

In operation 2720, encoded image data of a current picture assigned to amaximum coding unit, and information about a coded depth and a codingmode according to maximum coding units are extracted from the parsedbitstream. Information about an interpolation filter required to performsub-pel-unit motion compensation may be extracted from the encodinginformation.

Information about the coded depth and the coding mode may be extractedfrom the encoding information. According to the information about thecoded depth and the coding mode, a maximum coding unit may be split intocoding units having a tree structure. Also, according to informationabout a tree structure of transformation units included in the extractedinformation, transformation units having a tree structure according totransformation depths in the coding units may be determined.

In operation 2730, by using the information about the coded depth andthe coding mode according to each maximum coding unit, image data ofeach maximum coding unit may be decoded based on the coding units havinga tree structure, prediction units, and the transformation units havinga tree structure. Since a current coding unit is decoded based on theinformation about the coded depth and the coding mode, a current codingunit may be inversely transformed by using a transformation unitdetermined from among the transformation units having a tree structure.

Encoded picture data may be decoded by performing various decodingoperations such as motion compensation and intra prediction on eachprediction unit or partition of the coding unit based on the codingmode.

Specifically, if encoded residual data and reference data are extractedbased on pixels interpolated in a sub-pel unit, motion compensation on acurrent prediction unit or a current partition may be performed based onthe pixels interpolated in sub-pel units. From among interpolationfilters for generating a sub-pel-unit pixel value, an interpolationfilter may be differently selected based on a sub-pel-unit interpolationlocation. The interpolation filter may be selected as a symmetric orasymmetric interpolation filter according to an interpolation location.The interpolation filter may be an odd- or even-number-tap interpolationfilter.

In order to efficiently perform image interpolation, interpolationfilter coefficients may be selectively determined. From amonginterpolation filter coefficients previously stored in memory, a desiredinterpolation filter may be selected according to a sub-pel-unitinterpolation location, a smoothness, the number of filter taps, a bitdepth, a scaling ratio, a basis function of interpolation filteringbased on transformation, a window filter size, and a color component,and interpolation may be performed to generate the sub-pel-unit pixelvalue.

A reference picture and a reference region are determined by using thereference data, and the sub-pel-unit pixel value may be generated byperforming interpolation filtering on two or more integer-pel-unitreference pixels of the reference picture. Motion compensation may beperformed on the current prediction unit or the current partition bycombining the generated sub-pel-unit pixel value and the residual data,and thus prediction decoding may be performed.

Because each maximum coding unit is decoded, image data in a spatialdomain may be restored, and a picture and a video that includes apicture sequence may be restored. The restored video may be reproducedby a reproduction apparatus, may be stored in a storage medium, or maybe transmitted in a network.

The exemplary embodiments may be written as computer programs and may beimplemented in general-use digital computers that execute the programsusing a transitory or non-transitory computer readable recording medium.Examples of the non-transitory computer readable recording mediuminclude magnetic storage media (e.g., ROM, floppy disks, hard disks,etc.) and optical recording media (e.g., CD-ROMs, or DVDs).

While the present inventive concept has been particularly shown anddescribed with reference to exemplary embodiments thereof, it will beunderstood by those of ordinary skill in the art that various changes inform and details may be made therein without departing from the spiritand scope of the present inventive concept as defined by the appendedclaims. The exemplary embodiments should be considered in a descriptivesense only and not for purposes of limitation. Therefore, the scope ofthe present inventive concept is defined not by the detailed descriptionbut by the appended claims, and all differences within the scope will beconstrued as being included in the present inventive concept.

What is claimed is:
 1. A method of motion compensation, the methodcomprising: determining, in a luma reference picture, a luma referenceblock for prediction of a current block, by using a luma motion vectorof the current block; generating a luma sample of a ¼-pixel location ora ¾-pixel location included in the luma reference block by applying a7-tap filter to luma samples of an integer pixel location of the lumareference picture; determining, in a chroma reference picture, a chromareference block for prediction of a current block, by using a chromamotion vector of the current block; and generating a chroma sample of a⅛-pixel location or a 4/8-pixel location included in the chromareference block by applying a 4-tap filter to chroma samples of aninteger pixel location of the chroma reference picture, wherein the7-tap filter comprises seven filter coefficients, the 4-tap filtercomprises four filter coefficients, and filter coefficients of the 7-tapfilter for generating the luma sample of the ¼-pixel location arearranged in reverse order against filter coefficients of the 7-tapfilter for generating the luma sample of the ¾-pixel location.
 2. Themethod of claim 1, wherein the generating of the luma sample comprises:scaling the luma sample generated by applying the 7-tap filter by usinga luma scaling factor so that a sum of coefficients of the 7-tap filteris
 1. 3. The method of claim 1, wherein the generating of the at leastone chroma sample comprises: scaling the chroma sample generated byapplying the 4-tap filter by using a chroma scaling factor so that a sumof coefficients of the 4-tap filter is 1.